TSTP Solution File: SWB104+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB104+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 08:32:20 EDT 2022
% Result : Theorem 0.85s 0.82s
% Output : Proof 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWB104+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 20:30:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.85/0.82 % SZS status Theorem
% 0.85/0.82 % SZS output start Proof
% 0.85/0.82 tff(icext_type, type, (
% 0.85/0.82 icext: ( $i * $i ) > $o)).
% 0.85/0.82 tff(tptp_fun_Y2_43_type, type, (
% 0.85/0.82 tptp_fun_Y2_43: ( $i * $i * $i ) > $i)).
% 0.85/0.82 tff(uri_ex_p_type, type, (
% 0.85/0.82 uri_ex_p: $i)).
% 0.85/0.82 tff(uri_ex_c_type, type, (
% 0.85/0.82 uri_ex_c: $i)).
% 0.85/0.82 tff(tptp_fun_X_67_type, type, (
% 0.85/0.82 tptp_fun_X_67: ( $i * $i ) > $i)).
% 0.85/0.82 tff(uri_ex_z3_type, type, (
% 0.85/0.82 uri_ex_z3: $i)).
% 0.85/0.82 tff(uri_owl_Thing_type, type, (
% 0.85/0.82 uri_owl_Thing: $i)).
% 0.85/0.82 tff(iext_type, type, (
% 0.85/0.82 iext: ( $i * $i * $i ) > $o)).
% 0.85/0.82 tff(tptp_fun_Y1_44_type, type, (
% 0.85/0.82 tptp_fun_Y1_44: ( $i * $i * $i ) > $i)).
% 0.85/0.82 tff(uri_ex_z2_type, type, (
% 0.85/0.82 uri_ex_z2: $i)).
% 0.85/0.82 tff(uri_owl_onClass_type, type, (
% 0.85/0.82 uri_owl_onClass: $i)).
% 0.85/0.82 tff(tptp_fun_X0_141_type, type, (
% 0.85/0.82 tptp_fun_X0_141: $i)).
% 0.85/0.82 tff(tptp_fun_X1_140_type, type, (
% 0.85/0.82 tptp_fun_X1_140: $i)).
% 0.85/0.82 tff(uri_rdf_rest_type, type, (
% 0.85/0.82 uri_rdf_rest: $i)).
% 0.85/0.82 tff(uri_ex_z1_type, type, (
% 0.85/0.82 uri_ex_z1: $i)).
% 0.85/0.82 tff(uri_rdf_first_type, type, (
% 0.85/0.82 uri_rdf_first: $i)).
% 0.85/0.82 tff(uri_owl_onProperty_type, type, (
% 0.85/0.82 uri_owl_onProperty: $i)).
% 0.85/0.82 tff(literal_typed_type, type, (
% 0.85/0.82 literal_typed: ( $i * $i ) > $i)).
% 0.85/0.82 tff(uri_xsd_nonNegativeInteger_type, type, (
% 0.85/0.82 uri_xsd_nonNegativeInteger: $i)).
% 0.85/0.82 tff(dat_str_1_type, type, (
% 0.85/0.82 dat_str_1: $i)).
% 0.85/0.82 tff(uri_owl_minQualifiedCardinality_type, type, (
% 0.85/0.82 uri_owl_minQualifiedCardinality: $i)).
% 0.85/0.82 tff(uri_owl_unionOf_type, type, (
% 0.85/0.82 uri_owl_unionOf: $i)).
% 0.85/0.82 tff(uri_rdf_nil_type, type, (
% 0.85/0.82 uri_rdf_nil: $i)).
% 0.85/0.82 tff(uri_owl_maxQualifiedCardinality_type, type, (
% 0.85/0.82 uri_owl_maxQualifiedCardinality: $i)).
% 0.85/0.82 tff(ic_type, type, (
% 0.85/0.82 ic: $i > $o)).
% 0.85/0.82 tff(tptp_fun_X_6_type, type, (
% 0.85/0.82 tptp_fun_X_6: ( $i * $i * $i ) > $i)).
% 0.85/0.82 tff(uri_owl_equivalentClass_type, type, (
% 0.85/0.82 uri_owl_equivalentClass: $i)).
% 0.85/0.82 tff(uri_rdf_List_type, type, (
% 0.85/0.82 uri_rdf_List: $i)).
% 0.85/0.82 tff(ir_type, type, (
% 0.85/0.82 ir: $i > $o)).
% 0.85/0.82 tff(tptp_fun_Y_42_type, type, (
% 0.85/0.82 tptp_fun_Y_42: ( $i * $i * $i ) > $i)).
% 0.85/0.82 tff(1,plain,
% 0.85/0.82 (?[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))),
% 0.85/0.82 inference(rewrite,[status(thm)],[])).
% 0.85/0.82 tff(2,plain,
% 0.85/0.82 (^[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))))),
% 0.85/0.83 inference(bind,[status(th)],[])).
% 0.85/0.83 tff(3,plain,
% 0.85/0.83 (?[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))),
% 0.85/0.83 inference(quant_intro,[status(thm)],[2])).
% 0.85/0.83 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/sandbox2/benchmark/theBenchmark.p','premise_rdfbased_sem_restrict_term_minmaxthing')).
% 0.85/0.83 tff(5,plain,
% 0.85/0.83 (?[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))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.85/0.83 tff(6,plain,
% 0.85/0.83 (?[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))),
% 0.85/0.83 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.85/0.83 tff(7,plain,(
% 0.85/0.83 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)),
% 0.85/0.83 inference(skolemize,[status(sab)],[6])).
% 0.85/0.83 tff(8,plain,
% 0.85/0.83 (iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)),
% 0.85/0.83 inference(and_elim,[status(thm)],[7])).
% 0.85/0.83 tff(9,plain,
% 0.85/0.83 (iext(uri_owl_onProperty, uri_ex_z2, uri_ex_p)),
% 0.85/0.83 inference(and_elim,[status(thm)],[7])).
% 0.85/0.83 tff(10,plain,
% 0.85/0.83 (iext(uri_owl_maxQualifiedCardinality, uri_ex_z2, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))),
% 0.85/0.83 inference(and_elim,[status(thm)],[7])).
% 0.85/0.83 tff(11,plain,
% 0.85/0.83 (^[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)))))))))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(12,plain,
% 0.85/0.84 (![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))))))))))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[11])).
% 0.85/0.84 tff(13,plain,
% 0.85/0.84 (^[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)))))))))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(14,plain,
% 0.85/0.84 (![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))))))))))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[13])).
% 0.85/0.84 tff(15,plain,
% 0.85/0.84 (![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))))))))))),
% 0.85/0.84 inference(transitivity,[status(thm)],[14, 12])).
% 0.85/0.84 tff(16,plain,
% 0.85/0.84 (^[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))))))))))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(17,plain,
% 0.85/0.84 (![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))))))))))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[16])).
% 0.85/0.84 tff(18,plain,
% 0.85/0.84 (![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))))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(19,plain,
% 0.85/0.84 (^[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))))))),
% 0.85/0.84 inference(bind,[status(th)],[])).
% 0.85/0.84 tff(20,plain,
% 0.85/0.84 (![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))))),
% 0.85/0.84 inference(quant_intro,[status(thm)],[19])).
% 0.85/0.84 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/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_restrict_maxqcr_object_001')).
% 0.85/0.84 tff(22,plain,
% 0.85/0.84 (![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))))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.85/0.84 tff(23,plain,
% 0.85/0.84 (![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))))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.85/0.84 tff(24,plain,(
% 0.85/0.84 ![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)))))))),
% 0.85/0.84 inference(skolemize,[status(sab)],[23])).
% 0.85/0.84 tff(25,plain,
% 0.85/0.84 (![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))))))))))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.85/0.84 tff(26,plain,
% 0.85/0.84 (![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))))))))))),
% 0.85/0.84 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.85/0.84 tff(27,plain,
% 0.85/0.84 (((~![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_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | ![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) | (~((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_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | ![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) | (~((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))))))))))),
% 0.85/0.84 inference(rewrite,[status(thm)],[])).
% 0.85/0.84 tff(28,plain,
% 0.85/0.84 (((~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) | (~((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_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | ![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) | (~((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))))))))))),
% 0.91/0.84 inference(rewrite,[status(thm)],[])).
% 0.91/0.84 tff(29,plain,
% 0.91/0.84 (^[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) | (~((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))))))))))),
% 0.91/0.84 inference(bind,[status(th)],[])).
% 0.91/0.84 tff(30,plain,
% 0.91/0.84 (![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) | (~((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)))))))))),
% 0.91/0.84 inference(quant_intro,[status(thm)],[29])).
% 0.91/0.84 tff(31,plain,
% 0.91/0.84 (((~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) | (~((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))))))))))),
% 0.91/0.84 inference(monotonicity,[status(thm)],[30])).
% 0.91/0.84 tff(32,plain,
% 0.91/0.84 (((~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_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | ![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) | (~((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))))))))))),
% 0.91/0.84 inference(transitivity,[status(thm)],[31, 28])).
% 0.91/0.84 tff(33,plain,
% 0.91/0.84 (((~![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_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | ![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) | (~((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)))))))))))),
% 0.91/0.85 inference(monotonicity,[status(thm)],[32])).
% 0.91/0.85 tff(34,plain,
% 0.91/0.85 (((~![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_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | ![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) | (~((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))))))))))),
% 0.91/0.85 inference(transitivity,[status(thm)],[33, 27])).
% 0.91/0.85 tff(35,plain,
% 0.91/0.85 ((~![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))))))))))),
% 0.91/0.85 inference(quant_inst,[status(thm)],[])).
% 0.91/0.85 tff(36,plain,
% 0.91/0.85 ((~![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_onProperty, uri_ex_z2, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z2, uri_ex_c)) | ![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) | (~((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)))))))))),
% 0.91/0.85 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.91/0.85 tff(37,plain,
% 0.91/0.85 (![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) | (~((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)))))))))),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[36, 26, 10, 9, 8])).
% 0.91/0.85 tff(38,plain,
% 0.91/0.85 ((~![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) | (~((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, 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)) | (~((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)))))))))),
% 0.91/0.85 inference(quant_inst,[status(thm)],[])).
% 0.91/0.85 tff(39,plain,
% 0.91/0.85 (~((~((~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)) | (~((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))))))))),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.91/0.85 tff(40,plain,
% 0.91/0.85 (((~((~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)) | (~((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))))))),
% 0.91/0.85 inference(tautology,[status(thm)],[])).
% 0.91/0.85 tff(41,plain,
% 0.91/0.85 (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)))))),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.91/0.85 tff(42,plain,
% 0.91/0.85 (iext(uri_rdf_rest, X1!140, X0!141)),
% 0.91/0.85 inference(and_elim,[status(thm)],[7])).
% 0.91/0.85 tff(43,plain,
% 0.91/0.85 (iext(uri_rdf_first, X1!140, uri_ex_z1)),
% 0.91/0.85 inference(and_elim,[status(thm)],[7])).
% 0.91/0.85 tff(44,plain,
% 0.91/0.85 (iext(uri_rdf_rest, X0!141, uri_rdf_nil)),
% 0.91/0.85 inference(and_elim,[status(thm)],[7])).
% 0.91/0.85 tff(45,plain,
% 0.91/0.85 (iext(uri_rdf_first, X0!141, uri_ex_z2)),
% 0.91/0.85 inference(and_elim,[status(thm)],[7])).
% 0.91/0.85 tff(46,plain,
% 0.91/0.85 (^[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)))))))))))))),
% 0.91/0.85 inference(bind,[status(th)],[])).
% 0.91/0.85 tff(47,plain,
% 0.91/0.85 (![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)))))))))))),
% 0.91/0.85 inference(quant_intro,[status(thm)],[46])).
% 0.91/0.85 tff(48,plain,
% 0.91/0.85 (^[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))))))))))),
% 0.91/0.85 inference(bind,[status(th)],[])).
% 0.91/0.85 tff(49,plain,
% 0.91/0.85 (![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)))))))))),
% 0.91/0.85 inference(quant_intro,[status(thm)],[48])).
% 0.91/0.85 tff(50,plain,
% 0.91/0.85 (^[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))))))))))),
% 0.91/0.85 inference(bind,[status(th)],[])).
% 0.91/0.85 tff(51,plain,
% 0.91/0.85 (![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)))))))))),
% 0.91/0.85 inference(quant_intro,[status(thm)],[50])).
% 0.91/0.85 tff(52,plain,
% 0.91/0.85 (![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)))))))))),
% 0.91/0.85 inference(transitivity,[status(thm)],[51, 49])).
% 0.91/0.85 tff(53,plain,
% 0.91/0.85 (^[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)))))))), 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(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)))))))))))),
% 0.91/0.85 inference(bind,[status(th)],[])).
% 0.91/0.85 tff(54,plain,
% 0.91/0.85 (![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)))))))))),
% 0.91/0.85 inference(quant_intro,[status(thm)],[53])).
% 0.91/0.85 tff(55,plain,
% 0.91/0.85 (^[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))))))))),
% 0.91/0.85 inference(bind,[status(th)],[])).
% 0.91/0.85 tff(56,plain,
% 0.91/0.85 (![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)))))))),
% 0.91/0.85 inference(quant_intro,[status(thm)],[55])).
% 0.91/0.85 tff(57,plain,
% 0.91/0.85 (![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))))))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(58,plain,
% 0.91/0.86 (^[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))))))))),
% 0.91/0.86 inference(bind,[status(th)],[])).
% 0.91/0.86 tff(59,plain,
% 0.91/0.86 (![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))))))),
% 0.91/0.86 inference(quant_intro,[status(thm)],[58])).
% 0.91/0.86 tff(60,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/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_bool_unionof_class_002')).
% 0.91/0.86 tff(61,plain,
% 0.91/0.86 (![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))))))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.91/0.86 tff(62,plain,
% 0.91/0.86 (![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))))))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.91/0.86 tff(63,plain,(
% 0.91/0.86 ![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)))))))))),
% 0.91/0.86 inference(skolemize,[status(sab)],[62])).
% 0.91/0.86 tff(64,plain,
% 0.91/0.86 (![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)))))))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.91/0.86 tff(65,plain,
% 0.91/0.86 (![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)))))))))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.91/0.86 tff(66,plain,
% 0.91/0.86 (![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)))))))))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[65, 52])).
% 0.91/0.86 tff(67,plain,
% 0.91/0.86 (![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)))))))))))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[66, 47])).
% 0.91/0.86 tff(68,plain,
% 0.91/0.86 (((~![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_z2)) | (~ic(uri_ex_z1)) | ((~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_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![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_z2)) | (~ic(uri_ex_z1)) | ((~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_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(69,plain,
% 0.91/0.86 (((~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_z2)) | (~ic(uri_ex_z1)) | ((~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_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![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_z2)) | (~ic(uri_ex_z1)) | ((~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_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(70,plain,
% 0.91/0.86 ((~((~(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_z2)) | (~ic(uri_ex_z1)) | ((~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_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))))))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(71,plain,
% 0.91/0.86 (((~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_z2)) | (~ic(uri_ex_z1)) | ((~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_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))),
% 0.91/0.86 inference(monotonicity,[status(thm)],[70])).
% 0.91/0.86 tff(72,plain,
% 0.91/0.86 (((~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_z2)) | (~ic(uri_ex_z1)) | ((~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_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))),
% 0.91/0.86 inference(transitivity,[status(thm)],[71, 69])).
% 0.91/0.86 tff(73,plain,
% 0.91/0.86 (((~![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_z2)) | (~ic(uri_ex_z1)) | ((~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_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))))))))),
% 0.91/0.86 inference(monotonicity,[status(thm)],[72])).
% 0.91/0.86 tff(74,plain,
% 0.91/0.86 (((~![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_z2)) | (~ic(uri_ex_z1)) | ((~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_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))))),
% 0.91/0.86 inference(transitivity,[status(thm)],[73, 68])).
% 0.91/0.86 tff(75,plain,
% 0.91/0.86 ((~![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)))))))))))),
% 0.91/0.86 inference(quant_inst,[status(thm)],[])).
% 0.91/0.86 tff(76,plain,
% 0.91/0.86 ((~![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_z2)) | (~ic(uri_ex_z1)) | ((~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_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))))))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.91/0.86 tff(77,plain,
% 0.91/0.86 (~((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | ((~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_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))))),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[76, 67, 45, 44, 43, 42])).
% 0.91/0.86 tff(78,plain,
% 0.91/0.86 (((~(iext(uri_owl_unionOf, uri_ex_z3, X1!140) | (~ic(uri_ex_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | ((~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_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![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_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(79,plain,
% 0.91/0.87 ((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.91/0.87 tff(80,plain,
% 0.91/0.87 (iext(uri_owl_unionOf, uri_ex_z3, X1!140)),
% 0.91/0.87 inference(and_elim,[status(thm)],[7])).
% 0.91/0.87 tff(81,plain,
% 0.91/0.87 ((~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![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_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(82,plain,
% 0.91/0.87 ((~((~iext(uri_owl_unionOf, uri_ex_z3, X1!140)) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))))) | (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X))))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.91/0.87 tff(83,plain,
% 0.91/0.87 (~((~ic(uri_ex_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.91/0.87 tff(84,plain,
% 0.91/0.87 (((~ic(uri_ex_z3)) | (~ic(uri_ex_z2)) | (~ic(uri_ex_z1)) | (~![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)))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(85,plain,
% 0.91/0.87 (![X: $i] : (icext(uri_ex_z3, X) <=> (icext(uri_ex_z2, X) | icext(uri_ex_z1, X)))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.91/0.87 tff(86,plain,
% 0.91/0.87 ((~![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))))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(87,plain,
% 0.91/0.87 (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)))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.91/0.87 tff(88,plain,
% 0.91/0.87 (^[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))))))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(89,plain,
% 0.91/0.87 (![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)))))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[88])).
% 0.91/0.87 tff(90,plain,
% 0.91/0.87 (^[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))))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(91,plain,
% 0.91/0.87 (![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)))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[90])).
% 0.91/0.87 tff(92,plain,
% 0.91/0.87 (^[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))))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(93,plain,
% 0.91/0.87 (![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)))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[92])).
% 0.91/0.87 tff(94,plain,
% 0.91/0.87 (![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)))))))),
% 0.91/0.87 inference(transitivity,[status(thm)],[93, 91])).
% 0.91/0.87 tff(95,plain,
% 0.91/0.87 (^[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))))))), 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(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)))))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(96,plain,
% 0.91/0.87 (![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)))))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[95])).
% 0.91/0.87 tff(97,plain,
% 0.91/0.87 (^[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))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(98,plain,
% 0.91/0.87 (![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)))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[97])).
% 0.91/0.87 tff(99,plain,
% 0.91/0.87 (![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))))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(100,plain,
% 0.91/0.87 (^[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)))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(101,plain,
% 0.91/0.87 (![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))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[100])).
% 0.91/0.87 tff(102,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/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_eqdis_equivalentclass')).
% 0.91/0.87 tff(103,plain,
% 0.91/0.87 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.91/0.87 tff(104,plain,
% 0.91/0.87 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.91/0.87 tff(105,plain,(
% 0.91/0.87 ![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)))))))),
% 0.91/0.87 inference(skolemize,[status(sab)],[104])).
% 0.91/0.87 tff(106,plain,
% 0.91/0.87 (![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)))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.91/0.87 tff(107,plain,
% 0.91/0.87 (![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)))))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[106, 96])).
% 0.91/0.87 tff(108,plain,
% 0.91/0.87 (![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)))))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[107, 94])).
% 0.91/0.87 tff(109,plain,
% 0.91/0.87 (![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)))))))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[108, 89])).
% 0.91/0.87 tff(110,plain,
% 0.91/0.87 ((~![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)))))))))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(111,plain,
% 0.91/0.87 (~((~(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))))))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.91/0.87 tff(112,plain,
% 0.91/0.87 (((~(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_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))))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(113,plain,
% 0.91/0.87 (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)))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.91/0.87 tff(114,plain,
% 0.91/0.87 (^[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))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(115,plain,
% 0.91/0.87 (![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)))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[114])).
% 0.91/0.87 tff(116,plain,
% 0.91/0.87 (^[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))))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(117,plain,
% 0.91/0.87 (![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)))))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[116])).
% 0.91/0.87 tff(118,plain,
% 0.91/0.87 (![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)))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(119,plain,
% 0.91/0.87 (^[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))))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(120,plain,
% 0.91/0.87 (![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)))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[119])).
% 0.91/0.87 tff(121,axiom,(![X: $i, Y: $i] : (iext(uri_owl_unionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_prop_unionof_ext')).
% 0.91/0.87 tff(122,plain,
% 0.91/0.87 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.91/0.87 tff(123,plain,
% 0.91/0.87 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.91/0.87 tff(124,plain,(
% 0.91/0.87 ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 0.91/0.87 inference(skolemize,[status(sab)],[123])).
% 0.91/0.87 tff(125,plain,
% 0.91/0.87 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.91/0.87 tff(126,plain,
% 0.91/0.87 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[125, 115])).
% 0.91/0.87 tff(127,plain,
% 0.91/0.87 (((~![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)))))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(128,plain,
% 0.91/0.87 ((~![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)))))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(129,plain,
% 0.91/0.87 ((~![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))))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.91/0.87 tff(130,plain,
% 0.91/0.87 (~((~ic(uri_ex_z3)) | (~icext(uri_rdf_List, X1!140)))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[129, 126, 80])).
% 0.91/0.87 tff(131,plain,
% 0.91/0.87 (((~ic(uri_ex_z3)) | (~icext(uri_rdf_List, X1!140))) | ic(uri_ex_z3)),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(132,plain,
% 0.91/0.87 (ic(uri_ex_z3)),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.91/0.87 tff(133,plain,
% 0.91/0.87 ((~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)) <=> (~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(134,axiom,(~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conclusion_rdfbased_sem_restrict_term_minmaxthing')).
% 0.91/0.87 tff(135,plain,
% 0.91/0.87 (~iext(uri_owl_equivalentClass, uri_ex_z3, uri_owl_Thing)),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.91/0.87 tff(136,plain,
% 0.91/0.87 (ic(uri_owl_Thing) <=> ic(uri_owl_Thing)),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(137,axiom,(ic(uri_owl_Thing)), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_class_thing_type')).
% 0.91/0.87 tff(138,plain,
% 0.91/0.87 (ic(uri_owl_Thing)),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.91/0.87 tff(139,plain,
% 0.91/0.87 ((~(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)) | ((~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)))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(140,plain,
% 0.91/0.87 ((~(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))))) | (~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)))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[139, 138, 135])).
% 0.91/0.87 tff(141,plain,
% 0.91/0.87 ((~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))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[140, 132, 113])).
% 0.91/0.87 tff(142,plain,
% 0.91/0.87 (^[X: $i] : refl((icext(uri_owl_Thing, X) <=> ir(X)) <=> (icext(uri_owl_Thing, X) <=> ir(X)))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(143,plain,
% 0.91/0.87 (![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X)) <=> ![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.91/0.87 inference(quant_intro,[status(thm)],[142])).
% 0.91/0.87 tff(144,plain,
% 0.91/0.87 (![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X)) <=> ![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(145,axiom,(![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_class_thing_ext')).
% 0.91/0.87 tff(146,plain,
% 0.91/0.87 (![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.91/0.87 tff(147,plain,(
% 0.91/0.87 ![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.91/0.87 inference(skolemize,[status(sab)],[146])).
% 0.91/0.87 tff(148,plain,
% 0.91/0.87 (![X: $i] : (icext(uri_owl_Thing, X) <=> ir(X))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.91/0.87 tff(149,plain,
% 0.91/0.87 ((~![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)))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(150,plain,
% 0.91/0.87 (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))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.91/0.87 tff(151,plain,
% 0.91/0.87 (^[X: $i] : refl(ir(X) <=> ir(X))),
% 0.91/0.87 inference(bind,[status(th)],[])).
% 0.91/0.87 tff(152,plain,
% 0.91/0.87 (![X: $i] : ir(X) <=> ![X: $i] : ir(X)),
% 0.91/0.87 inference(quant_intro,[status(thm)],[151])).
% 0.91/0.87 tff(153,plain,
% 0.91/0.87 (![X: $i] : ir(X) <=> ![X: $i] : ir(X)),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(154,axiom,(![X: $i] : ir(X)), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','simple_ir')).
% 0.91/0.87 tff(155,plain,
% 0.91/0.87 (![X: $i] : ir(X)),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.91/0.87 tff(156,plain,(
% 0.91/0.87 ![X: $i] : ir(X)),
% 0.91/0.87 inference(skolemize,[status(sab)],[155])).
% 0.91/0.87 tff(157,plain,
% 0.91/0.87 (![X: $i] : ir(X)),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.91/0.87 tff(158,plain,
% 0.91/0.87 ((~![X: $i] : ir(X)) | ir(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(159,plain,
% 0.91/0.87 (ir(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.91/0.87 tff(160,plain,
% 0.91/0.87 ((~(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)))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(161,plain,
% 0.91/0.87 (icext(uri_owl_Thing, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[160, 159, 150])).
% 0.91/0.87 tff(162,plain,
% 0.91/0.87 ((~((~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)))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(163,plain,
% 0.91/0.87 (~icext(uri_ex_z3, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[162, 161, 141])).
% 0.91/0.87 tff(164,plain,
% 0.91/0.87 ((~(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))))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(165,plain,
% 0.91/0.87 (~(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)))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[164, 163, 87])).
% 0.91/0.87 tff(166,plain,
% 0.91/0.87 ((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)))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(167,plain,
% 0.91/0.87 (~icext(uri_ex_z2, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.91/0.87 tff(168,plain,
% 0.91/0.87 ((~(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)))))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(169,plain,
% 0.91/0.87 ((~(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)))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.91/0.87 tff(170,plain,
% 0.91/0.87 (~((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))))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[169, 41])).
% 0.91/0.87 tff(171,plain,
% 0.91/0.87 (((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))),
% 0.91/0.87 inference(tautology,[status(thm)],[])).
% 0.91/0.87 tff(172,plain,
% 0.91/0.87 (icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.91/0.87 tff(173,plain,
% 0.91/0.87 (((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))),
% 0.91/0.88 inference(tautology,[status(thm)],[])).
% 0.91/0.88 tff(174,plain,
% 0.91/0.88 (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))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[173, 170])).
% 0.91/0.88 tff(175,plain,
% 0.91/0.88 (iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)),
% 0.91/0.88 inference(and_elim,[status(thm)],[7])).
% 0.91/0.88 tff(176,plain,
% 0.91/0.88 (iext(uri_owl_onProperty, uri_ex_z1, uri_ex_p)),
% 0.91/0.88 inference(and_elim,[status(thm)],[7])).
% 0.91/0.88 tff(177,plain,
% 0.91/0.88 (iext(uri_owl_minQualifiedCardinality, uri_ex_z1, literal_typed(dat_str_1, uri_xsd_nonNegativeInteger))),
% 0.91/0.88 inference(and_elim,[status(thm)],[7])).
% 0.91/0.88 tff(178,plain,
% 0.91/0.88 (^[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)))))))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(179,plain,
% 0.91/0.88 (![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))))))))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[178])).
% 0.91/0.88 tff(180,plain,
% 0.91/0.88 (^[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)))))))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(181,plain,
% 0.91/0.88 (![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))))))))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[180])).
% 0.91/0.88 tff(182,plain,
% 0.91/0.88 (![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))))))))),
% 0.91/0.88 inference(transitivity,[status(thm)],[181, 179])).
% 0.91/0.88 tff(183,plain,
% 0.91/0.88 (^[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))))))))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(184,plain,
% 0.91/0.88 (![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))))))))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[183])).
% 0.91/0.88 tff(185,plain,
% 0.91/0.88 (![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))))),
% 0.91/0.88 inference(rewrite,[status(thm)],[])).
% 0.91/0.88 tff(186,plain,
% 0.91/0.88 (^[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))))))),
% 0.91/0.88 inference(bind,[status(th)],[])).
% 0.91/0.88 tff(187,plain,
% 0.91/0.88 (![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))))),
% 0.91/0.88 inference(quant_intro,[status(thm)],[186])).
% 0.91/0.88 tff(188,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/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_restrict_minqcr_object_001')).
% 0.91/0.88 tff(189,plain,
% 0.91/0.88 (![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))))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.91/0.88 tff(190,plain,
% 0.91/0.88 (![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))))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.91/0.88 tff(191,plain,(
% 0.91/0.88 ![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))))))),
% 0.91/0.88 inference(skolemize,[status(sab)],[190])).
% 0.91/0.88 tff(192,plain,
% 0.91/0.88 (![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))))))))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.91/0.88 tff(193,plain,
% 0.91/0.88 (![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))))))))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[192, 182])).
% 0.91/0.88 tff(194,plain,
% 0.91/0.88 (((~![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_onProperty, uri_ex_z1, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | ![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_onProperty, uri_ex_z1, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | ![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))))))))),
% 0.91/0.88 inference(rewrite,[status(thm)],[])).
% 0.91/0.88 tff(195,plain,
% 0.91/0.88 (((~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_onProperty, uri_ex_z1, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | ![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))))))))),
% 0.91/0.88 inference(rewrite,[status(thm)],[])).
% 0.91/0.88 tff(196,plain,
% 0.91/0.88 (((~![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_onProperty, uri_ex_z1, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | ![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)))))))))),
% 0.91/0.88 inference(monotonicity,[status(thm)],[195])).
% 0.91/0.88 tff(197,plain,
% 0.91/0.88 (((~![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_onProperty, uri_ex_z1, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | ![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))))))))),
% 0.91/0.88 inference(transitivity,[status(thm)],[196, 194])).
% 0.91/0.88 tff(198,plain,
% 0.91/0.88 ((~![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))))))))),
% 0.91/0.88 inference(quant_inst,[status(thm)],[])).
% 0.91/0.88 tff(199,plain,
% 0.91/0.88 ((~![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_onProperty, uri_ex_z1, uri_ex_p)) | (~iext(uri_owl_onClass, uri_ex_z1, uri_ex_c)) | ![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)))))))),
% 0.91/0.88 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.91/0.88 tff(200,plain,
% 0.91/0.88 (![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)))))))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[199, 193, 177, 176, 175])).
% 0.91/0.88 tff(201,plain,
% 0.91/0.88 ((~![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)))))))) | (~((~((~icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | (~((~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_c, 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)))))))),
% 0.91/0.88 inference(quant_inst,[status(thm)],[])).
% 0.91/0.88 tff(202,plain,
% 0.91/0.88 (~((~((~icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | (~((~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_c, 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))))))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.91/0.88 tff(203,plain,
% 0.91/0.88 (((~((~icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))) | (~((~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_c, 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)))))) | (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))))),
% 0.91/0.88 inference(tautology,[status(thm)],[])).
% 0.91/0.88 tff(204,plain,
% 0.91/0.88 (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)))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.91/0.88 tff(205,plain,
% 0.91/0.88 ((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)))),
% 0.91/0.88 inference(tautology,[status(thm)],[])).
% 0.91/0.88 tff(206,plain,
% 0.91/0.88 (~icext(uri_ex_z1, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[205, 165])).
% 0.91/0.88 tff(207,plain,
% 0.91/0.88 ((~(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)))),
% 0.91/0.88 inference(tautology,[status(thm)],[])).
% 0.91/0.88 tff(208,plain,
% 0.91/0.88 ((~(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)))),
% 0.91/0.88 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.91/0.88 tff(209,plain,
% 0.91/0.88 (![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y)))),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[208, 204])).
% 0.91/0.90 tff(210,plain,
% 0.91/0.90 (((~![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))))),
% 0.91/0.90 inference(rewrite,[status(thm)],[])).
% 0.91/0.90 tff(211,plain,
% 0.91/0.90 ((~![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))))),
% 0.91/0.90 inference(quant_inst,[status(thm)],[])).
% 0.91/0.90 tff(212,plain,
% 0.91/0.90 ((~![Y: $i] : ((~icext(uri_ex_c, Y)) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), Y)))) | (~icext(uri_ex_c, tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), tptp_fun_Y2_43(tptp_fun_X_67(uri_owl_Thing, uri_ex_z3), uri_ex_c, uri_ex_p)))),
% 0.91/0.90 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.91/0.90 tff(213,plain,
% 0.91/0.90 ($false),
% 0.91/0.90 inference(unit_resolution,[status(thm)],[212, 209, 174, 172])).
% 0.91/0.90 % SZS output end Proof
%------------------------------------------------------------------------------