%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB104+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 : Sat Jun 21 05:29:52 AM UTC 2025
% Result : Theorem 0.55s 0.71s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWB104+1 : TPTP v9.0.0. Released v5.2.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n013.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 07:58:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.55/0.71 % SZS status Theorem
% 0.55/0.71 % SZS output start Proof
% 0.55/0.71 tff(icext_type, type, (
% 0.55/0.71 icext: ( $i * $i ) > $o)).
% 0.55/0.71 tff(tptp_fun_Y2_43_type, type, (
% 0.55/0.71 tptp_fun_Y2_43: ( $i * $i * $i ) > $i)).
% 0.55/0.71 tff(uri_ex_p_type, type, (
% 0.55/0.71 uri_ex_p: $i)).
% 0.55/0.71 tff(uri_ex_c_type, type, (
% 0.55/0.71 uri_ex_c: $i)).
% 0.55/0.71 tff(tptp_fun_X_67_type, type, (
% 0.55/0.71 tptp_fun_X_67: ( $i * $i ) > $i)).
% 0.55/0.71 tff(uri_ex_z3_type, type, (
% 0.55/0.71 uri_ex_z3: $i)).
% 0.55/0.71 tff(uri_owl_Thing_type, type, (
% 0.55/0.71 uri_owl_Thing: $i)).
% 0.55/0.71 tff(iext_type, type, (
% 0.55/0.71 iext: ( $i * $i * $i ) > $o)).
% 0.55/0.71 tff(tptp_fun_Y1_44_type, type, (
% 0.55/0.71 tptp_fun_Y1_44: ( $i * $i * $i ) > $i)).
% 0.55/0.71 tff(uri_ex_z2_type, type, (
% 0.55/0.71 uri_ex_z2: $i)).
% 0.55/0.71 tff(uri_owl_onClass_type, type, (
% 0.55/0.71 uri_owl_onClass: $i)).
% 0.55/0.71 tff(tptp_fun_X0_141_type, type, (
% 0.55/0.71 tptp_fun_X0_141: $i)).
% 0.55/0.71 tff(tptp_fun_X1_140_type, type, (
% 0.55/0.71 tptp_fun_X1_140: $i)).
% 0.55/0.71 tff(uri_rdf_rest_type, type, (
% 0.55/0.71 uri_rdf_rest: $i)).
% 0.55/0.71 tff(uri_ex_z1_type, type, (
% 0.55/0.71 uri_ex_z1: $i)).
% 0.55/0.71 tff(uri_rdf_first_type, type, (
% 0.55/0.71 uri_rdf_first: $i)).
% 0.55/0.71 tff(uri_owl_onProperty_type, type, (
% 0.55/0.71 uri_owl_onProperty: $i)).
% 0.55/0.71 tff(literal_typed_type, type, (
% 0.55/0.71 literal_typed: ( $i * $i ) > $i)).
% 0.55/0.71 tff(uri_xsd_nonNegativeInteger_type, type, (
% 0.55/0.71 uri_xsd_nonNegativeInteger: $i)).
% 0.55/0.71 tff(dat_str_1_type, type, (
% 0.55/0.71 dat_str_1: $i)).
% 0.55/0.71 tff(uri_owl_minQualifiedCardinality_type, type, (
% 0.55/0.71 uri_owl_minQualifiedCardinality: $i)).
% 0.55/0.71 tff(uri_owl_unionOf_type, type, (
% 0.55/0.71 uri_owl_unionOf: $i)).
% 0.55/0.71 tff(uri_rdf_nil_type, type, (
% 0.55/0.71 uri_rdf_nil: $i)).
% 0.55/0.71 tff(uri_owl_maxQualifiedCardinality_type, type, (
% 0.55/0.71 uri_owl_maxQualifiedCardinality: $i)).
% 0.55/0.71 tff(ic_type, type, (
% 0.55/0.71 ic: $i > $o)).
% 0.55/0.71 tff(tptp_fun_X_6_type, type, (
% 0.55/0.71 tptp_fun_X_6: ( $i * $i * $i ) > $i)).
% 0.55/0.71 tff(uri_owl_equivalentClass_type, type, (
% 0.55/0.71 uri_owl_equivalentClass: $i)).
% 0.55/0.71 tff(uri_rdf_List_type, type, (
% 0.55/0.71 uri_rdf_List: $i)).
% 0.55/0.71 tff(ir_type, type, (
% 0.55/0.71 ir: $i > $o)).
% 0.55/0.71 tff(tptp_fun_Y_42_type, type, (
% 0.55/0.71 tptp_fun_Y_42: ( $i * $i * $i ) > $i)).
% 0.55/0.71 tff(1,plain,
% 0.55/0.71 (?[X0: $i, X1: $i] : (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c) & iext(uri_rdf_first, X1, uri_ex_z1) & iext(uri_rdf_rest, X1, X0)) <=> ?[X0: $i, X1: $i] : (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c) & iext(uri_rdf_first, X1, uri_ex_z1) & iext(uri_rdf_rest, X1, X0))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(2,plain,
% 0.55/0.71 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c))), ((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) <=> ((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)))), rewrite(((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2))), ((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2)))), (((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) <=> ((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)))), rewrite(((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil))), (((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil)))), ((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) <=> ((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)))), rewrite(((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1))), ((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1)))), (((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) <=> ((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))))), rewrite(((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))), (((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))))), ((((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) <=> ((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)))), rewrite(((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p))), ((((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)))), (((((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) <=> ((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)))), rewrite(((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c))), (((((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)))), ((((((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) & iext(uri_rdf_first, X1, uri_ex_z1)) <=> ((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) & iext(uri_rdf_first, X1, uri_ex_z1)))), rewrite(((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) & iext(uri_rdf_first, X1, uri_ex_z1)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c) & iext(uri_rdf_first, X1, uri_ex_z1))), ((((((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) & iext(uri_rdf_first, X1, uri_ex_z1)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c) & iext(uri_rdf_first, X1, uri_ex_z1)))), (((((((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) & iext(uri_rdf_first, X1, uri_ex_z1)) & iext(uri_rdf_rest, X1, X0)) <=> ((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c) & iext(uri_rdf_first, X1, uri_ex_z1)) & iext(uri_rdf_rest, X1, X0)))), rewrite(((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c) & iext(uri_rdf_first, X1, uri_ex_z1)) & iext(uri_rdf_rest, X1, X0)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c) & iext(uri_rdf_first, X1, uri_ex_z1) & iext(uri_rdf_rest, X1, X0))), (((((((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) & iext(uri_rdf_first, X1, uri_ex_z1)) & iext(uri_rdf_rest, X1, X0)) <=> (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c) & iext(uri_rdf_first, X1, uri_ex_z1) & iext(uri_rdf_rest, X1, X0))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(3,plain,
% 0.55/0.72 (?[X0: $i, X1: $i] : ((((((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) & iext(uri_rdf_first, X1, uri_ex_z1)) & iext(uri_rdf_rest, X1, X0)) <=> ?[X0: $i, X1: $i] : (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c) & iext(uri_rdf_first, X1, uri_ex_z1) & iext(uri_rdf_rest, X1, X0))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[2])).
% 0.55/0.72 tff(4,axiom,(?[X0: $i, X1: $i] : ((((((((((iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) & iext(uri_rdf_first, X0, uri_ex_z2)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_unionOf, uri_ex_z3, X1)) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) & iext(uri_rdf_first, X1, uri_ex_z1)) & iext(uri_rdf_rest, X1, X0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','premise_rdfbased_sem_restrict_term_minmaxthing')).
% 0.55/0.72 tff(5,plain,
% 0.55/0.72 (?[X0: $i, X1: $i] : (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c) & iext(uri_rdf_first, X1, uri_ex_z1) & iext(uri_rdf_rest, X1, X0))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.55/0.72 tff(6,plain,
% 0.55/0.72 (?[X0: $i, X1: $i] : (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0, uri_ex_z2) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c) & iext(uri_rdf_first, X1, uri_ex_z1) & iext(uri_rdf_rest, X1, X0))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.55/0.72 tff(7,plain,(
% 0.55/0.72 iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z2, uri_ex_c) & iext(uri_rdf_first, X0!141, uri_ex_z2) & iext(uri_rdf_rest, X0!141, uri_rdf_nil) & iext(uri_owl_unionOf, uri_ex_z3, X1!140) & iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p) & iext(uri_owl_onClass, uri_ex_z1, uri_ex_c) & iext(uri_rdf_first, X1!140, uri_ex_z1) & iext(uri_rdf_rest, X1!140, X0!141)),
% 0.55/0.72 inference(skolemize,[status(sab)],[6])).
% 0.55/0.72 tff(8,plain,
% 0.55/0.72 (iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)),
% 0.55/0.72 inference(and_elim,[status(thm)],[7])).
% 0.55/0.72 tff(9,plain,
% 0.55/0.72 (iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)),
% 0.55/0.72 inference(and_elim,[status(thm)],[7])).
% 0.55/0.72 tff(10,plain,
% 0.55/0.72 (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))),
% 0.55/0.72 inference(and_elim,[status(thm)],[7])).
% 0.55/0.72 tff(11,plain,
% 0.55/0.72 (^[Z: $i, P: $i, C: $i] : refl(((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))))))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(12,plain,
% 0.55/0.72 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[11])).
% 0.55/0.72 tff(13,plain,
% 0.55/0.72 (^[Z: $i, P: $i, C: $i] : rewrite(((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))))))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(14,plain,
% 0.55/0.72 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[13])).
% 0.55/0.72 tff(15,plain,
% 0.55/0.72 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))),
% 0.55/0.72 inference(transitivity,[status(thm)],[14, 12])).
% 0.55/0.72 tff(16,plain,
% 0.55/0.72 (^[Z: $i, P: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C)) <=> (~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))))), ((~(iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) <=> (~(~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))))))), rewrite((~(~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))))), ((~(iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))))), quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite(((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))) <=> ((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))), trans(monotonicity(rewrite((~((~(iext(P, X, tptp_fun_Y1_44(X, C, P)) & icext(C, tptp_fun_Y1_44(X, C, P)) & iext(P, X, tptp_fun_Y2_43(X, C, P)) & icext(C, tptp_fun_Y2_43(X, C, P)))) | (tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)))) <=> (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))), ((icext(Z, X) | (~((~(iext(P, X, tptp_fun_Y1_44(X, C, P)) & icext(C, tptp_fun_Y1_44(X, C, P)) & iext(P, X, tptp_fun_Y2_43(X, C, P)) & icext(C, tptp_fun_Y2_43(X, C, P)))) | (tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P))))) <=> (icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))))), rewrite((icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))) <=> (icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))), ((icext(Z, X) | (~((~(iext(P, X, tptp_fun_Y1_44(X, C, P)) & icext(C, tptp_fun_Y1_44(X, C, P)) & iext(P, X, tptp_fun_Y2_43(X, C, P)) & icext(C, tptp_fun_Y2_43(X, C, P)))) | (tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P))))) <=> (icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))))), ((((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))) & (icext(Z, X) | (~((~(iext(P, X, tptp_fun_Y1_44(X, C, P)) & icext(C, tptp_fun_Y1_44(X, C, P)) & iext(P, X, tptp_fun_Y2_43(X, C, P)) & icext(C, tptp_fun_Y2_43(X, C, P)))) | (tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)))))) <=> (((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2)))) & (icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))), rewrite((((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2)))) & (icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))) <=> (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))))))), ((((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))) & (icext(Z, X) | (~((~(iext(P, X, tptp_fun_Y1_44(X, C, P)) & icext(C, tptp_fun_Y1_44(X, C, P)) & iext(P, X, tptp_fun_Y2_43(X, C, P)) & icext(C, tptp_fun_Y2_43(X, C, P)))) | (tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)))))) <=> (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))))))))), (![X: $i] : (((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))) & (icext(Z, X) | (~((~(iext(P, X, tptp_fun_Y1_44(X, C, P)) & icext(C, tptp_fun_Y1_44(X, C, P)) & iext(P, X, tptp_fun_Y2_43(X, C, P)) & icext(C, tptp_fun_Y2_43(X, C, P)))) | (tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)))))) <=> ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))), (((~(iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))) & (icext(Z, X) | (~((~(iext(P, X, tptp_fun_Y1_44(X, C, P)) & icext(C, tptp_fun_Y1_44(X, C, P)) & iext(P, X, tptp_fun_Y2_43(X, C, P)) & icext(C, tptp_fun_Y2_43(X, C, P)))) | (tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P))))))) <=> (((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))))))))), rewrite((((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P)))))))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))), (((~(iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))) & (icext(Z, X) | (~((~(iext(P, X, tptp_fun_Y1_44(X, C, P)) & icext(C, tptp_fun_Y1_44(X, C, P)) & iext(P, X, tptp_fun_Y2_43(X, C, P)) & icext(C, tptp_fun_Y2_43(X, C, P)))) | (tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P))))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(17,plain,
% 0.55/0.73 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))) & (icext(Z, X) | (~((~(iext(P, X, tptp_fun_Y1_44(X, C, P)) & icext(C, tptp_fun_Y1_44(X, C, P)) & iext(P, X, tptp_fun_Y2_43(X, C, P)) & icext(C, tptp_fun_Y2_43(X, C, P)))) | (tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[16])).
% 0.55/0.73 tff(18,plain,
% 0.55/0.73 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(19,plain,
% 0.55/0.73 (^[Z: $i, P: $i, C: $i] : trans(monotonicity(rewrite(((iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) & iext(uri_owl_onClass, Z, C)) <=> (iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))), quant_intro(proof_bind(^[X: $i] : rewrite((icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((((iext(P, X, Y1) & icext(C, Y1)) & iext(P, X, Y2)) & icext(C, Y2)) => (Y2 = Y1))) <=> (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))))), (![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((((iext(P, X, Y1) & icext(C, Y1)) & iext(P, X, Y2)) & icext(C, Y2)) => (Y2 = Y1))) <=> ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))))), ((((iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) & iext(uri_owl_onClass, Z, C)) => ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((((iext(P, X, Y1) & icext(C, Y1)) & iext(P, X, Y2)) & icext(C, Y2)) => (Y2 = Y1)))) <=> ((iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C)) => ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1)))))), rewrite(((iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C)) => ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1)))) <=> ((~(iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))))), ((((iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) & iext(uri_owl_onClass, Z, C)) => ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((((iext(P, X, Y1) & icext(C, Y1)) & iext(P, X, Y2)) & icext(C, Y2)) => (Y2 = Y1)))) <=> ((~(iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(20,plain,
% 0.55/0.73 (![Z: $i, P: $i, C: $i] : (((iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) & iext(uri_owl_onClass, Z, C)) => ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((((iext(P, X, Y1) & icext(C, Y1)) & iext(P, X, Y2)) & icext(C, Y2)) => (Y2 = Y1)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[19])).
% 0.55/0.73 tff(21,axiom,(![Z: $i, P: $i, C: $i] : (((iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) & iext(uri_owl_onClass, Z, C)) => ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((((iext(P, X, Y1) & icext(C, Y1)) & iext(P, X, Y2)) & icext(C, Y2)) => (Y2 = Y1))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_restrict_maxqcr_object_001')).
% 0.55/0.73 tff(22,plain,
% 0.55/0.73 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.55/0.73 tff(23,plain,
% 0.55/0.73 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.55/0.73 tff(24,plain,(
% 0.55/0.73 ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & icext(C, Y1) & iext(P, X, Y2) & icext(C, Y2))) | (Y2 = Y1))) & (icext(Z, X) | (~((~(iext(P, X, tptp_fun_Y1_44(X, C, P)) & icext(C, tptp_fun_Y1_44(X, C, P)) & iext(P, X, tptp_fun_Y2_43(X, C, P)) & icext(C, tptp_fun_Y2_43(X, C, P)))) | (tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)))))))),
% 0.55/0.73 inference(skolemize,[status(sab)],[23])).
% 0.55/0.73 tff(25,plain,
% 0.55/0.73 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.55/0.73 tff(26,plain,
% 0.55/0.73 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.55/0.73 tff(27,plain,
% 0.55/0.73 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))) | ((~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))) | (~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)))))))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(28,plain,
% 0.55/0.73 (((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))))))))) <=> ((~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)))))))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(29,plain,
% 0.55/0.73 (^[X: $i] : rewrite((~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~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_z2, X) | (~((tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))))))))) <=> (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)))))))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(30,plain,
% 0.55/0.73 (![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~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_z2, X) | (~((tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))))))))) <=> ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))))))))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[29])).
% 0.55/0.73 tff(31,plain,
% 0.55/0.73 (((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~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_z2, X) | (~((tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p)))))))))) <=> ((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)))))))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[30])).
% 0.55/0.73 tff(32,plain,
% 0.55/0.73 (((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~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_z2, X) | (~((tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p)))))))))) <=> ((~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)))))))))),
% 0.55/0.73 inference(transitivity,[status(thm)],[31, 28])).
% 0.55/0.73 tff(33,plain,
% 0.55/0.73 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))) | ((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~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_z2, X) | (~((tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))) | ((~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))))))))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[32])).
% 0.55/0.73 tff(34,plain,
% 0.55/0.73 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))) | ((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~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_z2, X) | (~((tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))) | (~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)))))))))),
% 0.55/0.73 inference(transitivity,[status(thm)],[33, 27])).
% 0.55/0.73 tff(35,plain,
% 0.55/0.73 ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))) | ((~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~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_z2, X) | (~((tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))))))))))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(36,plain,
% 0.55/0.73 ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_maxQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(C, Y2)) | (~iext(P, X, Y1)) | (~icext(C, Y1)) | (~iext(P, X, Y2))))) | (~(icext(Z, X) | (~((tptp_fun_Y2_43(X, C, P) = tptp_fun_Y1_44(X, C, P)) | (~iext(P, X, tptp_fun_Y1_44(X, C, P))) | (~icext(C, tptp_fun_Y1_44(X, C, P))) | (~iext(P, X, tptp_fun_Y2_43(X, C, P))) | (~icext(C, tptp_fun_Y2_43(X, C, P))))))))))) | (~iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)) | ![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))))))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.55/0.73 tff(37,plain,
% 0.55/0.73 (![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))))))))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[36, 26, 10, 9, 8])).
% 0.55/0.73 tff(38,plain,
% 0.55/0.73 (((~![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))))))))) | (~((~((~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y1))))) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))))))))) <=> ((~![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))))))))) | (~((~((~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y1))))) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))))))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(39,plain,
% 0.55/0.74 ((~((~((~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y1)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y2))))) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))))))) <=> (~((~((~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y1))))) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))))))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(40,plain,
% 0.55/0.74 (((~![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))))))))) | (~((~((~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y1)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y2))))) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))))))) <=> ((~![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))))))))) | (~((~((~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y1))))) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))))))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[39])).
% 0.55/0.74 tff(41,plain,
% 0.55/0.74 (((~![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))))))))) | (~((~((~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y1)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y2))))) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))))))) <=> ((~![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))))))))) | (~((~((~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y1))))) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))))))))),
% 0.55/0.74 inference(transitivity,[status(thm)],[40, 38])).
% 0.55/0.74 tff(42,plain,
% 0.55/0.74 ((~![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))))))))) | (~((~((~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y1)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y2))))) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))))))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(43,plain,
% 0.55/0.74 ((~![X: $i] : (~((~((~icext(uri_ex_z2, X)) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, X, Y1)) | (~iext(uri_ex_p, X, Y2))))) | (~(icext(uri_ex_z2, X) | (~((~icext(uri_ex_c, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))) | (tptp_fun_Y2_43(X, uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(X, uri_ex_c, uri_ex_p))))))))) | (~((~((~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y1))))) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))))))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.55/0.74 tff(44,plain,
% 0.55/0.74 (~((~((~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y1))))) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[43, 37])).
% 0.55/0.74 tff(45,plain,
% 0.55/0.74 (((~((~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | ![Y1: $i, Y2: $i] : ((Y2 = Y1) | (~icext(uri_ex_c, Y1)) | (~icext(uri_ex_c, Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y2)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y1))))) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))))))) | (icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))))),
% 0.55/0.74 inference(tautology,[status(thm)],[])).
% 0.55/0.74 tff(46,plain,
% 0.55/0.74 (icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.55/0.74 tff(47,plain,
% 0.55/0.74 (iext(uri_rdf_rest, X1!140, X0!141)),
% 0.55/0.74 inference(and_elim,[status(thm)],[7])).
% 0.55/0.74 tff(48,plain,
% 0.55/0.74 (iext(uri_rdf_first, X1!140, uri_ex_z1)),
% 0.55/0.74 inference(and_elim,[status(thm)],[7])).
% 0.55/0.74 tff(49,plain,
% 0.55/0.74 (iext(uri_rdf_rest, X0!141, uri_rdf_nil)),
% 0.55/0.74 inference(and_elim,[status(thm)],[7])).
% 0.55/0.74 tff(50,plain,
% 0.55/0.74 (iext(uri_rdf_first, X0!141, uri_ex_z2)),
% 0.55/0.74 inference(and_elim,[status(thm)],[7])).
% 0.55/0.74 tff(51,plain,
% 0.55/0.74 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))))))), rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(52,plain,
% 0.55/0.74 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[51])).
% 0.55/0.74 tff(53,plain,
% 0.55/0.74 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : refl(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(54,plain,
% 0.55/0.74 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[53])).
% 0.55/0.74 tff(55,plain,
% 0.55/0.74 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(56,plain,
% 0.55/0.74 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[55])).
% 0.55/0.74 tff(57,plain,
% 0.55/0.74 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 0.55/0.74 inference(transitivity,[status(thm)],[56, 54])).
% 0.55/0.74 tff(58,plain,
% 0.55/0.74 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) <=> ((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))), trans(monotonicity(rewrite((~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))) <=> (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))), ((iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))), rewrite((iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))), ((iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))), ((((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> (((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))), rewrite((((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))), ((((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))) <=> (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))))), rewrite((((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(59,plain,
% 0.55/0.74 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[58])).
% 0.55/0.74 tff(60,plain,
% 0.55/0.74 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(61,plain,
% 0.55/0.74 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[60])).
% 0.55/0.74 tff(62,plain,
% 0.55/0.74 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(63,plain,
% 0.55/0.74 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite((iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X))))) <=> (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X)))))) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))),
% 0.55/0.75 inference(bind,[status(th)],[])).
% 0.55/0.75 tff(64,plain,
% 0.55/0.75 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 0.55/0.75 inference(quant_intro,[status(thm)],[63])).
% 0.55/0.75 tff(65,axiom,(![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_bool_unionof_class_002')).
% 0.55/0.75 tff(66,plain,
% 0.55/0.75 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.55/0.75 tff(67,plain,
% 0.55/0.75 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.55/0.75 tff(68,plain,(
% 0.55/0.75 ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 0.55/0.75 inference(skolemize,[status(sab)],[67])).
% 0.55/0.75 tff(69,plain,
% 0.55/0.75 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.55/0.75 tff(70,plain,
% 0.55/0.75 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.55/0.75 tff(71,plain,
% 0.55/0.75 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[70, 57])).
% 0.55/0.75 tff(72,plain,
% 0.55/0.75 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[71, 52])).
% 0.55/0.75 tff(73,plain,
% 0.55/0.75 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(74,plain,
% 0.55/0.75 (((~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))))))) <=> ((~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(75,plain,
% 0.55/0.75 ((~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z3)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z3)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))) <=> (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(76,plain,
% 0.55/0.75 (((~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z3)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z3)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))))))) <=> ((~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[75])).
% 0.55/0.75 tff(77,plain,
% 0.55/0.75 (((~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z3)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z3)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))))))) <=> ((~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))),
% 0.55/0.75 inference(transitivity,[status(thm)],[76, 74])).
% 0.55/0.75 tff(78,plain,
% 0.55/0.75 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z3)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z3)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))))))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[77])).
% 0.55/0.75 tff(79,plain,
% 0.55/0.75 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z3)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z3)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))),
% 0.55/0.75 inference(transitivity,[status(thm)],[78, 73])).
% 0.55/0.75 tff(80,plain,
% 0.55/0.75 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z3)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z3)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(81,plain,
% 0.55/0.75 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, X0!141, uri_ex_z2)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~iext(uri_rdf_first, X1!140, uri_ex_z1)) | (~iext(uri_rdf_rest, X1!140, X0!141)) | (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))))))),
% 0.60/0.75 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.60/0.75 tff(82,plain,
% 0.60/0.75 (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))),
% 0.60/0.75 inference(unit_resolution,[status(thm)],[81, 72, 50, 49, 48, 47])).
% 0.60/0.75 tff(83,plain,
% 0.60/0.75 (((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~(icext(uri_ex_z3, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) <=> (icext(uri_ex_z1, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3)) | icext(uri_ex_z2, tptp_fun_X_6(uri_ex_z2, uri_ex_z1, uri_ex_z3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))))) | ((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))),
% 0.60/0.75 inference(tautology,[status(thm)],[])).
% 0.60/0.75 tff(84,plain,
% 0.60/0.75 ((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))),
% 0.60/0.75 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.60/0.75 tff(85,plain,
% 0.60/0.75 (iext(uri_owl_unionOf, uri_ex_z3, X1!140)),
% 0.60/0.75 inference(and_elim,[status(thm)],[7])).
% 0.60/0.75 tff(86,plain,
% 0.60/0.75 ((~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))) | (~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))),
% 0.60/0.75 inference(tautology,[status(thm)],[])).
% 0.60/0.75 tff(87,plain,
% 0.60/0.75 ((~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))),
% 0.60/0.75 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.60/0.75 tff(88,plain,
% 0.60/0.75 (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))),
% 0.60/0.75 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.60/0.75 tff(89,plain,
% 0.60/0.75 (((~ic(uri_ex_z3)) | (~ic(uri_ex_z1)) | (~ic(uri_ex_z2)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))) | ![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))),
% 0.60/0.75 inference(tautology,[status(thm)],[])).
% 0.60/0.75 tff(90,plain,
% 0.60/0.75 (![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))),
% 0.60/0.75 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.60/0.75 tff(91,plain,
% 0.60/0.75 ((~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))) | (icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> (icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))))),
% 0.60/0.75 inference(quant_inst,[status(thm)],[])).
% 0.60/0.75 tff(92,plain,
% 0.60/0.75 (icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> (icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))),
% 0.60/0.75 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.60/0.75 tff(93,plain,
% 0.60/0.75 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))))))),
% 0.60/0.75 inference(bind,[status(th)],[])).
% 0.60/0.75 tff(94,plain,
% 0.60/0.75 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 0.60/0.75 inference(quant_intro,[status(thm)],[93])).
% 0.60/0.75 tff(95,plain,
% 0.60/0.75 (^[C1: $i, C2: $i] : refl((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))))),
% 0.60/0.75 inference(bind,[status(th)],[])).
% 0.60/0.75 tff(96,plain,
% 0.60/0.75 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 0.60/0.75 inference(quant_intro,[status(thm)],[95])).
% 0.60/0.75 tff(97,plain,
% 0.60/0.75 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))))),
% 0.60/0.75 inference(bind,[status(th)],[])).
% 0.60/0.75 tff(98,plain,
% 0.60/0.75 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 0.60/0.75 inference(quant_intro,[status(thm)],[97])).
% 0.60/0.75 tff(99,plain,
% 0.60/0.75 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 0.60/0.75 inference(transitivity,[status(thm)],[98, 96])).
% 0.60/0.75 tff(100,plain,
% 0.60/0.75 (^[C1: $i, C2: $i] : trans(monotonicity(rewrite(((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))), trans(monotonicity(rewrite((~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))) <=> (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))), rewrite((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))), ((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) <=> (((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))), rewrite((((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))), ((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))))),
% 0.60/0.75 inference(bind,[status(th)],[])).
% 0.60/0.75 tff(101,plain,
% 0.60/0.75 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[100])).
% 0.60/0.76 tff(102,plain,
% 0.60/0.76 (^[C1: $i, C2: $i] : rewrite((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(103,plain,
% 0.60/0.76 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> ![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[102])).
% 0.60/0.76 tff(104,plain,
% 0.60/0.76 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(105,plain,
% 0.60/0.76 (^[C1: $i, C2: $i] : rewrite((iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(106,plain,
% 0.60/0.76 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[105])).
% 0.60/0.76 tff(107,axiom,(![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_eqdis_equivalentclass')).
% 0.60/0.76 tff(108,plain,
% 0.60/0.76 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.60/0.76 tff(109,plain,
% 0.60/0.76 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.60/0.76 tff(110,plain,(
% 0.60/0.76 ![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 0.60/0.76 inference(skolemize,[status(sab)],[109])).
% 0.60/0.76 tff(111,plain,
% 0.60/0.76 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.60/0.76 tff(112,plain,
% 0.60/0.76 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[111, 101])).
% 0.60/0.76 tff(113,plain,
% 0.60/0.76 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[112, 99])).
% 0.60/0.76 tff(114,plain,
% 0.60/0.76 (![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[113, 94])).
% 0.60/0.76 tff(115,plain,
% 0.60/0.76 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) | (~((~![X: $i] : (icext(uri_ex_z3, X) <=> icext(uri_owl_Thing, X))) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) | (~((~![X: $i] : (icext(uri_ex_z3, X) <=> icext(uri_owl_Thing, X))) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)))))))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(116,plain,
% 0.60/0.76 ((~((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_owl_Thing)) | (~ic(uri_ex_z3)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~ic(uri_ex_z3)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> icext(uri_owl_Thing, X))))))))) <=> (~((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) | (~((~![X: $i] : (icext(uri_ex_z3, X) <=> icext(uri_owl_Thing, X))) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing))))))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(117,plain,
% 0.60/0.76 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_owl_Thing)) | (~ic(uri_ex_z3)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~ic(uri_ex_z3)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> icext(uri_owl_Thing, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) | (~((~![X: $i] : (icext(uri_ex_z3, X) <=> icext(uri_owl_Thing, X))) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)))))))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[116])).
% 0.60/0.76 tff(118,plain,
% 0.60/0.76 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_owl_Thing)) | (~ic(uri_ex_z3)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~ic(uri_ex_z3)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> icext(uri_owl_Thing, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) | (~((~![X: $i] : (icext(uri_ex_z3, X) <=> icext(uri_owl_Thing, X))) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)))))))))),
% 0.60/0.76 inference(transitivity,[status(thm)],[117, 115])).
% 0.60/0.76 tff(119,plain,
% 0.60/0.76 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_owl_Thing)) | (~ic(uri_ex_z3)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) | (~((~ic(uri_owl_Thing)) | (~ic(uri_ex_z3)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> icext(uri_owl_Thing, X)))))))))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(120,plain,
% 0.60/0.76 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) | (~((~![X: $i] : (icext(uri_ex_z3, X) <=> icext(uri_owl_Thing, X))) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing))))))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.60/0.76 tff(121,plain,
% 0.60/0.76 (~((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) | (~((~![X: $i] : (icext(uri_ex_z3, X) <=> icext(uri_owl_Thing, X))) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)))))))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[120, 114])).
% 0.60/0.76 tff(122,plain,
% 0.60/0.76 (((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) | (~((~![X: $i] : (icext(uri_ex_z3, X) <=> icext(uri_owl_Thing, X))) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing))))))) | (iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(123,plain,
% 0.60/0.76 (iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.60/0.76 tff(124,plain,
% 0.60/0.76 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(125,plain,
% 0.60/0.76 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[124])).
% 0.60/0.76 tff(126,plain,
% 0.60/0.76 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(127,plain,
% 0.60/0.76 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[126])).
% 0.60/0.76 tff(128,plain,
% 0.60/0.76 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(129,plain,
% 0.60/0.76 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_unionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(130,plain,
% 0.60/0.76 (![X: $i, Y: $i] : (iext(uri_owl_unionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[129])).
% 0.60/0.76 tff(131,axiom,(![X: $i, Y: $i] : (iext(uri_owl_unionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_prop_unionof_ext')).
% 0.60/0.76 tff(132,plain,
% 0.60/0.76 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.60/0.76 tff(133,plain,
% 0.60/0.76 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.60/0.76 tff(134,plain,(
% 0.60/0.76 ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.60/0.76 inference(skolemize,[status(sab)],[133])).
% 0.60/0.76 tff(135,plain,
% 0.60/0.76 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.60/0.76 tff(136,plain,
% 0.60/0.76 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[135, 125])).
% 0.60/0.76 tff(137,plain,
% 0.60/0.76 (((~![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~icext(uri_rdf_List, X1!140)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~icext(uri_rdf_List, X1!140)))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(138,plain,
% 0.60/0.76 ((~![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~icext(uri_rdf_List, X1!140)))))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(139,plain,
% 0.60/0.76 ((~![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~icext(uri_rdf_List, X1!140))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.60/0.76 tff(140,plain,
% 0.60/0.76 (~((~ic(uri_ex_z3)) | (~icext(uri_rdf_List, X1!140)))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[139, 136, 85])).
% 0.60/0.76 tff(141,plain,
% 0.60/0.76 (((~ic(uri_ex_z3)) | (~icext(uri_rdf_List, X1!140))) | ic(uri_ex_z3)),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(142,plain,
% 0.60/0.76 (ic(uri_ex_z3)),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.60/0.76 tff(143,plain,
% 0.60/0.76 ((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) <=> (~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(144,axiom,(~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conclusion_rdfbased_sem_restrict_term_minmaxthing')).
% 0.60/0.76 tff(145,plain,
% 0.60/0.76 (~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.60/0.76 tff(146,plain,
% 0.60/0.76 (ic(uri_owl_Thing) <=> ic(uri_owl_Thing)),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(147,axiom,(ic(uri_owl_Thing)), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_class_thing_type')).
% 0.60/0.76 tff(148,plain,
% 0.60/0.76 (ic(uri_owl_Thing)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.60/0.76 tff(149,plain,
% 0.60/0.76 ((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(150,plain,
% 0.60/0.76 ((~(iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing) | (~ic(uri_ex_z3)) | (~ic(uri_owl_Thing)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))))) | (~ic(uri_ex_z3)) | (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[149, 148, 145])).
% 0.60/0.76 tff(151,plain,
% 0.60/0.76 (~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[150, 142, 123])).
% 0.60/0.76 tff(152,plain,
% 0.60/0.76 (^[X: $i] : refl((icext(uri_owl_Thing, X) <=> ir(X)) <=> (icext(uri_owl_Thing, X) <=> ir(X)))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(153,plain,
% 0.60/0.76 (![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X)) <=> ![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[152])).
% 0.60/0.76 tff(154,plain,
% 0.60/0.76 (![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X)) <=> ![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(155,axiom,(![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_class_thing_ext')).
% 0.60/0.76 tff(156,plain,
% 0.60/0.76 (![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.60/0.76 tff(157,plain,(
% 0.60/0.76 ![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.60/0.76 inference(skolemize,[status(sab)],[156])).
% 0.60/0.76 tff(158,plain,
% 0.60/0.76 (![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.60/0.76 tff(159,plain,
% 0.60/0.76 ((~![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))) | (icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> ir(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(160,plain,
% 0.60/0.76 (icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> ir(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.60/0.76 tff(161,plain,
% 0.60/0.76 (^[X: $i] : refl(ir(X) <=> ir(X))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(162,plain,
% 0.60/0.76 (![X: $i] : ir(X) <=> ![X: $i] : ir(X)),
% 0.60/0.76 inference(quant_intro,[status(thm)],[161])).
% 0.60/0.76 tff(163,plain,
% 0.60/0.76 (![X: $i] : ir(X) <=> ![X: $i] : ir(X)),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(164,axiom,(![X: $i] : ir(X)), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','simple_ir')).
% 0.60/0.76 tff(165,plain,
% 0.60/0.76 (![X: $i] : ir(X)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.60/0.76 tff(166,plain,(
% 0.60/0.76 ![X: $i] : ir(X)),
% 0.60/0.76 inference(skolemize,[status(sab)],[165])).
% 0.60/0.76 tff(167,plain,
% 0.60/0.76 (![X: $i] : ir(X)),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.60/0.76 tff(168,plain,
% 0.60/0.76 ((~![X: $i] : ir(X)) | ir(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(169,plain,
% 0.60/0.76 (ir(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.60/0.76 tff(170,plain,
% 0.60/0.76 ((~(icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> ir(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))) | icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~ir(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(171,plain,
% 0.60/0.76 (icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[170, 169, 160])).
% 0.60/0.76 tff(172,plain,
% 0.60/0.76 ((icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | (~icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | (~icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(173,plain,
% 0.60/0.76 (~icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[172, 171, 151])).
% 0.60/0.76 tff(174,plain,
% 0.60/0.76 ((~(icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) <=> (icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))))) | icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(175,plain,
% 0.60/0.76 (~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[174, 173, 92])).
% 0.60/0.76 tff(176,plain,
% 0.60/0.76 ((icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | (~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(177,plain,
% 0.60/0.76 (~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.60/0.76 tff(178,plain,
% 0.60/0.76 ((~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))))) | icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(179,plain,
% 0.60/0.76 ((~(icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))))) | (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.60/0.76 tff(180,plain,
% 0.60/0.76 (~((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[179, 46])).
% 0.60/0.76 tff(181,plain,
% 0.60/0.76 (((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))) | icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(182,plain,
% 0.60/0.76 (icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.60/0.76 tff(183,plain,
% 0.60/0.76 (((tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p) = tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y1_44(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))) | iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))),
% 0.60/0.76 inference(tautology,[status(thm)],[])).
% 0.60/0.76 tff(184,plain,
% 0.60/0.76 (iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[183, 180])).
% 0.60/0.76 tff(185,plain,
% 0.60/0.76 (iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)),
% 0.60/0.76 inference(and_elim,[status(thm)],[7])).
% 0.60/0.76 tff(186,plain,
% 0.60/0.76 (iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)),
% 0.60/0.76 inference(and_elim,[status(thm)],[7])).
% 0.60/0.76 tff(187,plain,
% 0.60/0.76 (iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))),
% 0.60/0.76 inference(and_elim,[status(thm)],[7])).
% 0.60/0.76 tff(188,plain,
% 0.60/0.76 (^[Z: $i, P: $i, C: $i] : refl(((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(189,plain,
% 0.60/0.76 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[188])).
% 0.60/0.76 tff(190,plain,
% 0.60/0.76 (^[Z: $i, P: $i, C: $i] : rewrite(((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(191,plain,
% 0.60/0.76 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[190])).
% 0.60/0.76 tff(192,plain,
% 0.60/0.76 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))),
% 0.60/0.76 inference(transitivity,[status(thm)],[191, 189])).
% 0.60/0.76 tff(193,plain,
% 0.60/0.76 (^[Z: $i, P: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C)) <=> (~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))))), ((~(iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) <=> (~(~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))))))), rewrite((~(~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))))), ((~(iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))))), quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite(((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) <=> ((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))), rewrite((icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))) <=> (icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))), ((((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))) <=> (((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P)))))) & (icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))), rewrite((((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P)))))) & (icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))) <=> (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))), ((((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))) <=> (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))))), (![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))) <=> ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))), (((~(iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))))) <=> (((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))))), rewrite((((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))), (((~(iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))))),
% 0.60/0.76 inference(bind,[status(th)],[])).
% 0.60/0.76 tff(194,plain,
% 0.60/0.76 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))),
% 0.60/0.76 inference(quant_intro,[status(thm)],[193])).
% 0.60/0.76 tff(195,plain,
% 0.60/0.76 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(196,plain,
% 0.60/0.77 (^[Z: $i, P: $i, C: $i] : trans(monotonicity(rewrite(((iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) & iext(uri_owl_onClass, Z, C)) <=> (iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))), ((((iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) & iext(uri_owl_onClass, Z, C)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ((iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))))), rewrite(((iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ((~(iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))), ((((iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) & iext(uri_owl_onClass, Z, C)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ((~(iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(197,plain,
% 0.60/0.77 (![Z: $i, P: $i, C: $i] : (((iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) & iext(uri_owl_onClass, Z, C)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[196])).
% 0.60/0.77 tff(198,axiom,(![Z: $i, P: $i, C: $i] : (((iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P)) & iext(uri_owl_onClass, Z, C)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_restrict_minqcr_object_001')).
% 0.60/0.77 tff(199,plain,
% 0.60/0.77 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.60/0.77 tff(200,plain,
% 0.60/0.77 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.60/0.77 tff(201,plain,(
% 0.60/0.77 ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger)) & iext(uri_owl_onProperty, Z, P) & iext(uri_owl_onClass, Z, C))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))))),
% 0.60/0.77 inference(skolemize,[status(sab)],[200])).
% 0.60/0.77 tff(202,plain,
% 0.60/0.77 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[201, 194])).
% 0.60/0.77 tff(203,plain,
% 0.60/0.77 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[202, 192])).
% 0.60/0.77 tff(204,plain,
% 0.60/0.77 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | ![X: $i] : (~((~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z1, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | (~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | ![X: $i] : (~((~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z1, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(205,plain,
% 0.60/0.77 (((~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z1, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p)))))))))) <=> ((~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | ![X: $i] : (~((~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z1, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(206,plain,
% 0.60/0.77 (^[X: $i] : rewrite((~((~((~icext(uri_ex_z1, X)) | (~((~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))) | (~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))))) <=> (~((~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z1, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(207,plain,
% 0.60/0.77 (![X: $i] : (~((~((~icext(uri_ex_z1, X)) | (~((~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))) | (~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))))) <=> ![X: $i] : (~((~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z1, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p)))))))))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[206])).
% 0.60/0.77 tff(208,plain,
% 0.60/0.77 (((~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(uri_ex_z1, X)) | (~((~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))) | (~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y)))))))) <=> ((~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z1, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[207])).
% 0.60/0.77 tff(209,plain,
% 0.60/0.77 (((~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(uri_ex_z1, X)) | (~((~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))) | (~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y)))))))) <=> ((~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | ![X: $i] : (~((~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z1, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[208, 205])).
% 0.60/0.77 tff(210,plain,
% 0.60/0.77 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(uri_ex_z1, X)) | (~((~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))) | (~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | ![X: $i] : (~((~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z1, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p)))))))))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[209])).
% 0.60/0.77 tff(211,plain,
% 0.60/0.77 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(uri_ex_z1, X)) | (~((~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))) | (~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | (~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | ![X: $i] : (~((~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z1, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[210, 204])).
% 0.60/0.77 tff(212,plain,
% 0.60/0.77 ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(uri_ex_z1, X)) | (~((~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))))))) | (~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(213,plain,
% 0.60/0.77 ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_onClass, Z, C)) | (~iext(uri_owl_minQualifiedCardinality, Z, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | (~iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | (~iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)) | ![X: $i] : (~((~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z1, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p)))))))))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.60/0.77 tff(214,plain,
% 0.60/0.77 (![X: $i] : (~((~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z1, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p)))))))))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[213, 203, 187, 186, 185])).
% 0.60/0.77 tff(215,plain,
% 0.60/0.77 ((~![X: $i] : (~((~(icext(uri_ex_z1, X) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, X, Y))))) | (~((~icext(uri_ex_z1, X)) | (~((~icext(uri_ex_c, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, X, tptp_fun_Y_42(X, uri_ex_c, uri_ex_p)))))))))) | (~((~(icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y))))) | (~((~icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | (~((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y_42(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))))))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(216,plain,
% 0.60/0.77 (~((~(icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y))))) | (~((~icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | (~((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y_42(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))))))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.60/0.77 tff(217,plain,
% 0.60/0.77 (((~(icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y))))) | (~((~icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | (~((~icext(uri_ex_c, tptp_fun_Y_42(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y_42(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))))))) | (icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y))))),
% 0.60/0.77 inference(tautology,[status(thm)],[])).
% 0.60/0.77 tff(218,plain,
% 0.60/0.77 (icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y)))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.60/0.77 tff(219,plain,
% 0.60/0.77 ((icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | (~icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)))),
% 0.60/0.77 inference(tautology,[status(thm)],[])).
% 0.60/0.77 tff(220,plain,
% 0.60/0.77 (~icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[219, 175])).
% 0.60/0.77 tff(221,plain,
% 0.60/0.77 ((~(icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y))))) | icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y)))),
% 0.60/0.77 inference(tautology,[status(thm)],[])).
% 0.60/0.77 tff(222,plain,
% 0.60/0.77 ((~(icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3)) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y))))) | ![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y)))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.60/0.77 tff(223,plain,
% 0.60/0.77 (![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y)))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[222, 218])).
% 0.60/0.77 tff(224,plain,
% 0.60/0.77 (((~![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y)))) | ((~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))) <=> ((~![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y)))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(225,plain,
% 0.60/0.79 ((~![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y)))) | ((~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(226,plain,
% 0.60/0.79 ((~![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y)))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.60/0.79 tff(227,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[226, 223, 184, 182])).
% 0.60/0.79 % SZS output end Proof
% 0.60/0.79 % E exiting
%------------------------------------------------------------------------------