TSTP Solution File: SWB084+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB084+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 08:32:14 EDT 2022
% Result : Theorem 0.79s 0.75s
% Output : Proof 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 54
% Syntax : Number of formulae : 109 ( 23 unt; 18 typ; 0 def)
% Number of atoms : 3715 ( 728 equ)
% Maximal formula atoms : 124 ( 40 avg)
% Number of connectives : 6463 (2909 ~;2923 |; 521 &)
% ( 98 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 14 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 70 ( 70 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 8 >; 14 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-3 aty)
% Number of variables : 873 ( 813 !; 34 ?; 873 :)
% Comments :
%------------------------------------------------------------------------------
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(uri_ex_w_type,type,
uri_ex_w: $i ).
tff(uri_ex_p_type,type,
uri_ex_p: $i ).
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(uri_ex_c_type,type,
uri_ex_c: $i ).
tff(tptp_fun_Y2_45_type,type,
tptp_fun_Y2_45: ( $i * $i * $i ) > $i ).
tff(tptp_fun_Y1_46_type,type,
tptp_fun_Y1_46: ( $i * $i * $i ) > $i ).
tff(uri_ex_z_type,type,
uri_ex_z: $i ).
tff(tptp_fun_Y3_47_type,type,
tptp_fun_Y3_47: ( $i * $i * $i ) > $i ).
tff(tptp_fun_Y2_48_type,type,
tptp_fun_Y2_48: ( $i * $i * $i ) > $i ).
tff(tptp_fun_Y1_49_type,type,
tptp_fun_Y1_49: ( $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_2_type,type,
dat_str_2: $i ).
tff(uri_owl_qualifiedCardinality_type,type,
uri_owl_qualifiedCardinality: $i ).
tff(uri_rdf_type_type,type,
uri_rdf_type: $i ).
tff(1,plain,
( iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
<=> iext(uri_owl_onClass,uri_ex_z,uri_ex_c) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
( iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
& iext(uri_rdf_type,uri_ex_w,uri_ex_z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_rdfbased_sem_restrict_exactqcr_inst_obj_two) ).
tff(3,plain,
( iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
& iext(uri_owl_onClass,uri_ex_z,uri_ex_c) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
iext(uri_owl_onClass,uri_ex_z,uri_ex_c),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
iext(uri_owl_onClass,uri_ex_z,uri_ex_c),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
<=> iext(uri_owl_onProperty,uri_ex_z,uri_ex_p) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_z,uri_ex_p) ),
inference(and_elim,[status(thm)],[3]) ).
tff(8,plain,
iext(uri_owl_onProperty,uri_ex_z,uri_ex_p),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
iext(uri_owl_onProperty,uri_ex_z,uri_ex_p),
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,plain,
( iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
<=> iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger)) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger)),
inference(and_elim,[status(thm)],[7]) ).
tff(12,plain,
iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger)),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [Z: $i,P: $i,C: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) )
<=> ~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) ))),
( ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) )),
( ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) ) )),
rewrite(
( ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) ) )),
( ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [Z: $i,P: $i,C: $i] :
refl(
( ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
^ [Z: $i,P: $i,C: $i] :
rewrite(
( ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) ),
inference(transitivity,[status(thm)],[18,16]) ).
tff(20,plain,
^ [Z: $i,P: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
<=> ~ ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C) ) )),
( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
<=> ~ ~ ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C) ) )),
rewrite(
( ~ ~ ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C) ) )),
( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C) ) )),
quant_intro(
proof_bind(
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y1_46(X,C,P))
& icext(C,tptp_fun_Y1_46(X,C,P))
& iext(P,X,tptp_fun_Y2_45(X,C,P))
& icext(C,tptp_fun_Y2_45(X,C,P))
& ( tptp_fun_Y1_46(X,C,P) != tptp_fun_Y2_45(X,C,P) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) )
<=> ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) ) )),
trans(
monotonicity(
quant_intro(
proof_bind(
^ [Y1: $i,Y2: $i] :
trans(
monotonicity(
rewrite(
( ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
<=> ~ ( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )),
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
<=> ~ ~ ( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )),
rewrite(
( ~ ~ ( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
<=> ( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )),
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
<=> ( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ))),
( ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
<=> ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )),
rewrite(
( ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) )
<=> ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) )),
( ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) )
<=> ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) )),
rewrite(
( ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) )
<=> ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) )),
( ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) )
<=> ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) )),
( ( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y1_46(X,C,P))
& icext(C,tptp_fun_Y1_46(X,C,P))
& iext(P,X,tptp_fun_Y2_45(X,C,P))
& icext(C,tptp_fun_Y2_45(X,C,P))
& ( tptp_fun_Y1_46(X,C,P) != tptp_fun_Y2_45(X,C,P) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )
<=> ( ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )),
rewrite(
( ( ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) )
<=> ~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )),
( ( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y1_46(X,C,P))
& icext(C,tptp_fun_Y1_46(X,C,P))
& iext(P,X,tptp_fun_Y2_45(X,C,P))
& icext(C,tptp_fun_Y2_45(X,C,P))
& ( tptp_fun_Y1_46(X,C,P) != tptp_fun_Y2_45(X,C,P) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )
<=> ~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ))),
( ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y1_46(X,C,P))
& icext(C,tptp_fun_Y1_46(X,C,P))
& iext(P,X,tptp_fun_Y2_45(X,C,P))
& icext(C,tptp_fun_Y2_45(X,C,P))
& ( tptp_fun_Y1_46(X,C,P) != tptp_fun_Y2_45(X,C,P) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )),
( ( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y1_46(X,C,P))
& icext(C,tptp_fun_Y1_46(X,C,P))
& iext(P,X,tptp_fun_Y2_45(X,C,P))
& icext(C,tptp_fun_Y2_45(X,C,P))
& ( tptp_fun_Y1_46(X,C,P) != tptp_fun_Y2_45(X,C,P) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) )),
rewrite(
( ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) )),
( ( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y1_46(X,C,P))
& icext(C,tptp_fun_Y1_46(X,C,P))
& iext(P,X,tptp_fun_Y2_45(X,C,P))
& icext(C,tptp_fun_Y2_45(X,C,P))
& ( tptp_fun_Y1_46(X,C,P) != tptp_fun_Y2_45(X,C,P) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y1_46(X,C,P))
& icext(C,tptp_fun_Y1_46(X,C,P))
& iext(P,X,tptp_fun_Y2_45(X,C,P))
& icext(C,tptp_fun_Y2_45(X,C,P))
& ( tptp_fun_Y1_46(X,C,P) != tptp_fun_Y2_45(X,C,P) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
^ [Z: $i,P: $i,C: $i] :
rewrite(
( ( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y1_46(X,C,P))
& icext(C,tptp_fun_Y1_46(X,C,P))
& iext(P,X,tptp_fun_Y2_45(X,C,P))
& icext(C,tptp_fun_Y2_45(X,C,P))
& ( tptp_fun_Y1_46(X,C,P) != tptp_fun_Y2_45(X,C,P) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) )
<=> ( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y1_46(X,C,P))
& icext(C,tptp_fun_Y1_46(X,C,P))
& iext(P,X,tptp_fun_Y2_45(X,C,P))
& icext(C,tptp_fun_Y2_45(X,C,P))
& ( tptp_fun_Y1_46(X,C,P) != tptp_fun_Y2_45(X,C,P) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y1_46(X,C,P))
& icext(C,tptp_fun_Y1_46(X,C,P))
& iext(P,X,tptp_fun_Y2_45(X,C,P))
& icext(C,tptp_fun_Y2_45(X,C,P))
& ( tptp_fun_Y1_46(X,C,P) != tptp_fun_Y2_45(X,C,P) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y1_46(X,C,P))
& icext(C,tptp_fun_Y1_46(X,C,P))
& iext(P,X,tptp_fun_Y2_45(X,C,P))
& icext(C,tptp_fun_Y2_45(X,C,P))
& ( tptp_fun_Y1_46(X,C,P) != tptp_fun_Y2_45(X,C,P) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
^ [Z: $i,P: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
<=> ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) )
=> ( ( Y3 = Y1 )
| ( Y3 = Y2 ) ) ) ) )
<=> ( icext(Z,X)
<=> ( ? [Y1: $i,Y2: $i] :
( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) ) ))),
( ! [X: $i] :
( icext(Z,X)
<=> ( ? [Y1: $i,Y2: $i] :
( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) )
=> ( ( Y3 = Y1 )
| ( Y3 = Y2 ) ) ) ) )
<=> ! [X: $i] :
( icext(Z,X)
<=> ( ? [Y1: $i,Y2: $i] :
( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) ) )),
( ( ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) )
=> ( ( Y3 = Y1 )
| ( Y3 = Y2 ) ) ) ) ) )
<=> ( ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) ) ) )),
rewrite(
( ( ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) ) )
<=> ( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) ) ) )),
( ( ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) )
=> ( ( Y3 = Y1 )
| ( Y3 = Y2 ) ) ) ) ) )
<=> ( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [Z: $i,P: $i,C: $i] :
( ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) )
=> ( ( Y3 = Y1 )
| ( Y3 = Y2 ) ) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [Z: $i,P: $i,C: $i] :
( ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) )
=> ( ( Y3 = Y1 )
| ( Y3 = Y2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_restrict_exactqcr_object_002) ).
tff(28,plain,
! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,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)
& ( Y1 != Y2 ) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y1_46(X,C,P))
& icext(C,tptp_fun_Y1_46(X,C,P))
& iext(P,X,tptp_fun_Y2_45(X,C,P))
& icext(C,tptp_fun_Y2_45(X,C,P))
& ( tptp_fun_Y1_46(X,C,P) != tptp_fun_Y2_45(X,C,P) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ( iext(P,X,tptp_fun_Y1_46(X,C,P))
& icext(C,tptp_fun_Y1_46(X,C,P))
& iext(P,X,tptp_fun_Y2_45(X,C,P))
& icext(C,tptp_fun_Y2_45(X,C,P))
& ( tptp_fun_Y1_46(X,C,P) != tptp_fun_Y2_45(X,C,P) )
& ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& iext(P,X,Y3)
& icext(C,Y3) ) ) ) )
& ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2)
& ( Y1 != Y2 ) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ ( iext(P,X,tptp_fun_Y1_49(X,C,P))
& icext(C,tptp_fun_Y1_49(X,C,P))
& iext(P,X,tptp_fun_Y2_48(X,C,P))
& icext(C,tptp_fun_Y2_48(X,C,P))
& iext(P,X,tptp_fun_Y3_47(X,C,P))
& icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ),
inference(modus_ponens,[status(thm)],[31,21]) ).
tff(33,plain,
! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) ) ) ) ),
inference(modus_ponens,[status(thm)],[32,19]) ).
tff(34,plain,
! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) ),
inference(modus_ponens,[status(thm)],[33,14]) ).
tff(35,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) ) )
<=> ( ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2) ) ) )
<=> ~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2) ) ) ) )
<=> ( ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) ) ) ),
inference(transitivity,[status(thm)],[39,36]) ).
tff(41,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) ) ) ),
inference(transitivity,[status(thm)],[41,35]) ).
tff(43,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_qualifiedCardinality,Z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onClass,Z,C)
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ~ ( ( tptp_fun_Y1_46(X,C,P) = tptp_fun_Y2_45(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_46(X,C,P))
| ~ icext(C,tptp_fun_Y1_46(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_45(X,C,P))
| ~ icext(C,tptp_fun_Y2_45(X,C,P))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2)
| ~ icext(C,Y2)
| ~ iext(P,X,Y3)
| ~ icext(C,Y3) ) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y2_48(X,C,P) )
| ( tptp_fun_Y3_47(X,C,P) = tptp_fun_Y1_49(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_49(X,C,P))
| ~ icext(C,tptp_fun_Y1_49(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_48(X,C,P))
| ~ icext(C,tptp_fun_Y2_48(X,C,P))
| ~ iext(P,X,tptp_fun_Y3_47(X,C,P))
| ~ icext(C,tptp_fun_Y3_47(X,C,P)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) ) )
| ~ iext(uri_owl_qualifiedCardinality,uri_ex_z,literal_typed(dat_str_2,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
| ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) ),
inference(unit_resolution,[status(thm)],[44,34,12,9,5]) ).
tff(46,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) )
| ~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) )
| ~ ( icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) )
| ~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) )
| ~ ( icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,uri_ex_w)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ iext(uri_ex_p,uri_ex_w,Y2) )
| ~ ( ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p)) ) ) )
<=> ~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) )
| ~ ( icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) )
| ~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,uri_ex_w)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ iext(uri_ex_p,uri_ex_w,Y2) )
| ~ ( ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) )
| ~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) )
| ~ ( icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2) ) ) ) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) )
| ~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,uri_ex_w)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ iext(uri_ex_p,uri_ex_w,Y2) )
| ~ ( ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) )
| ~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) )
| ~ ( icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2) ) ) ) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) )
| ~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,uri_ex_w)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ iext(uri_ex_p,uri_ex_w,Y2) )
| ~ ( ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_z,X)
| ~ ( ( tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(X,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p,X,Y2)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y3)
| ~ icext(uri_ex_c,Y3) ) ) )
| ~ ( icext(uri_ex_z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p,X,Y1)
| ~ iext(uri_ex_p,X,Y2) )
| ~ ( ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,X,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(X,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,X,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(X,uri_ex_c,uri_ex_p)) ) ) )
| ~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) )
| ~ ( icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2) ) ) ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) )
| ~ ( icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2) ) ) ),
inference(unit_resolution,[status(thm)],[51,45]) ).
tff(53,plain,
( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) )
| ~ ( icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_49(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_48(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y3_47(uri_ex_w,uri_ex_c,uri_ex_p)) )
| ! [Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ iext(uri_ex_p,uri_ex_w,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2) ) )
| ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(54,plain,
( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) ),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
^ [X: $i,C: $i] :
refl(
( ( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
<=> ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',rdfs_cext_def) ).
tff(59,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [X: $i,C: $i] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) )
| ( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> icext(uri_ex_z,uri_ex_w) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> icext(uri_ex_z,uri_ex_w) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> iext(uri_rdf_type,uri_ex_w,uri_ex_z) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
iext(uri_rdf_type,uri_ex_w,uri_ex_z),
inference(and_elim,[status(thm)],[2]) ).
tff(66,plain,
iext(uri_rdf_type,uri_ex_w,uri_ex_z),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( ~ ( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> icext(uri_ex_z,uri_ex_w) )
| ~ iext(uri_rdf_type,uri_ex_w,uri_ex_z)
| icext(uri_ex_z,uri_ex_w) ),
inference(tautology,[status(thm)],]) ).
tff(68,plain,
( ~ ( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
<=> icext(uri_ex_z,uri_ex_w) )
| icext(uri_ex_z,uri_ex_w) ),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
icext(uri_ex_z,uri_ex_w),
inference(unit_resolution,[status(thm)],[68,63]) ).
tff(70,plain,
( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) )
| ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(71,plain,
( ~ ( ~ icext(uri_ex_z,uri_ex_w)
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) )
| ~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ) ),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
~ ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ),
inference(unit_resolution,[status(thm)],[71,54]) ).
tff(73,plain,
( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ) ),
inference(tautology,[status(thm)],]) ).
tff(74,plain,
! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) ),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)) ),
inference(tautology,[status(thm)],]) ).
tff(76,plain,
icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)),
inference(unit_resolution,[status(thm)],[75,72]) ).
tff(77,plain,
( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)) ),
inference(tautology,[status(thm)],]) ).
tff(78,plain,
iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)),
inference(unit_resolution,[status(thm)],[77,72]) ).
tff(79,plain,
( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p)) ),
inference(tautology,[status(thm)],]) ).
tff(80,plain,
icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p)),
inference(unit_resolution,[status(thm)],[79,72]) ).
tff(81,plain,
( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p)) ),
inference(tautology,[status(thm)],]) ).
tff(82,plain,
iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p)),
inference(unit_resolution,[status(thm)],[81,72]) ).
tff(83,plain,
( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) != tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) ) ),
inference(tautology,[status(thm)],]) ).
tff(84,plain,
tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) != tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p),
inference(unit_resolution,[status(thm)],[83,72]) ).
tff(85,plain,
( ( ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)) )
<=> ( ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)) )
<=> ( ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)) )
<=> ( ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)) ) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( ( ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)) )
<=> ( ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)) ) ),
inference(transitivity,[status(thm)],[87,85]) ).
tff(89,plain,
( ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [Y1: $i,Y2: $i,Y3: $i] :
( ( Y3 = Y2 )
| ( Y3 = Y1 )
| ~ iext(uri_ex_p,uri_ex_w,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y2)
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ icext(uri_ex_c,Y3)
| ~ iext(uri_ex_p,uri_ex_w,Y1) )
| ( tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p) = tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p) )
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y1_46(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p))
| ~ icext(uri_ex_c,tptp_fun_Y2_45(uri_ex_w,uri_ex_c,uri_ex_p)) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
$false,
inference(unit_resolution,[status(thm)],[90,84,82,80,78,76,74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWB084+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 20:25:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.79/0.75 % SZS status Theorem
% 0.79/0.75 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------