%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB026+2 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:40 AM UTC 2025
% Result : Theorem 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWB026+2 : TPTP v9.0.0. Released v5.2.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 07:52:07 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 tff(tptp_fun_X2_2_type, type, (
% 0.19/0.50 tptp_fun_X2_2: $i > $i)).
% 0.19/0.50 tff(uri_ex_p_type, type, (
% 0.19/0.50 uri_ex_p: $i)).
% 0.19/0.50 tff(tptp_fun_X1_3_type, type, (
% 0.19/0.50 tptp_fun_X1_3: $i > $i)).
% 0.19/0.50 tff(uri_ex_w_type, type, (
% 0.19/0.50 uri_ex_w: $i)).
% 0.19/0.50 tff(icext_type, type, (
% 0.19/0.50 icext: ( $i * $i ) > $o)).
% 0.19/0.50 tff(tptp_fun_BNODE_x1_7_type, type, (
% 0.19/0.50 tptp_fun_BNODE_x1_7: $i)).
% 0.19/0.50 tff(ic_type, type, (
% 0.19/0.50 ic: $i > $o)).
% 0.19/0.50 tff(iext_type, type, (
% 0.19/0.50 iext: ( $i * $i * $i ) > $o)).
% 0.19/0.50 tff(tptp_fun_BNODE_l1_5_type, type, (
% 0.19/0.50 tptp_fun_BNODE_l1_5: $i)).
% 0.19/0.50 tff(uri_owl_oneOf_type, type, (
% 0.19/0.50 uri_owl_oneOf: $i)).
% 0.19/0.50 tff(tptp_fun_X_0_type, type, (
% 0.19/0.50 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.19/0.50 tff(uri_rdf_nil_type, type, (
% 0.19/0.50 uri_rdf_nil: $i)).
% 0.19/0.50 tff(uri_rdf_rest_type, type, (
% 0.19/0.50 uri_rdf_rest: $i)).
% 0.19/0.50 tff(tptp_fun_BNODE_l2_4_type, type, (
% 0.19/0.50 tptp_fun_BNODE_l2_4: $i)).
% 0.19/0.50 tff(uri_ex_u_type, type, (
% 0.19/0.50 uri_ex_u: $i)).
% 0.19/0.50 tff(uri_rdf_first_type, type, (
% 0.19/0.50 uri_rdf_first: $i)).
% 0.19/0.50 tff(tptp_fun_BNODE_x2_6_type, type, (
% 0.19/0.50 tptp_fun_BNODE_x2_6: $i)).
% 0.19/0.50 tff(uri_rdfs_range_type, type, (
% 0.19/0.50 uri_rdfs_range: $i)).
% 0.19/0.50 tff(uri_rdfs_domain_type, type, (
% 0.19/0.50 uri_rdfs_domain: $i)).
% 0.19/0.50 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.50 tptp_fun_Y_1: $i > $i)).
% 0.19/0.50 tff(ip_type, type, (
% 0.19/0.50 ip: $i > $o)).
% 0.19/0.50 tff(uri_rdf_Property_type, type, (
% 0.19/0.50 uri_rdf_Property: $i)).
% 0.19/0.50 tff(uri_rdf_type_type, type, (
% 0.19/0.50 uri_rdf_type: $i)).
% 0.19/0.50 tff(uri_owl_InverseFunctionalProperty_type, type, (
% 0.19/0.50 uri_owl_InverseFunctionalProperty: $i)).
% 0.19/0.50 tff(1,plain,
% 0.19/0.50 (?[BNODE_x1: $i, BNODE_x2: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_u) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> ?[BNODE_x1: $i, BNODE_x2: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_u) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(2,plain,
% 0.19/0.50 (^[BNODE_x1: $i, BNODE_x2: $i, BNODE_l1: $i, BNODE_l2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) <=> (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w))), ((((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) <=> ((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil))), ((((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)))), (((((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)) <=> ((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)) <=> (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2))), (((((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)) <=> (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)))), ((((((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2)) <=> ((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2)) <=> (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2))), ((((((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2)) <=> (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2)))), (((((((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_u)) <=> ((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_u)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_u)) <=> (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_u))), (((((((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_u)) <=> (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_u)))), ((((((((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_u)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> ((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_u)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_u)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_u) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))), ((((((((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_u)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_u) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(3,plain,
% 0.19/0.50 (?[BNODE_x1: $i, BNODE_x2: $i, BNODE_l1: $i, BNODE_l2: $i] : (((((((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_u)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> ?[BNODE_x1: $i, BNODE_x2: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_u) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.50 tff(4,axiom,(?[BNODE_x1: $i, BNODE_x2: $i, BNODE_l1: $i, BNODE_l2: $i] : (((((((iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1)) & iext(uri_rdf_first, BNODE_l1, uri_ex_w)) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil)) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2)) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, uri_ex_u)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_premise_fullish_026_Inferred_Property_Characteristics_I')).
% 0.19/0.50 tff(5,plain,
% 0.19/0.50 (?[BNODE_x1: $i, BNODE_x2: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_u) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.50 tff(6,plain,
% 0.19/0.50 (?[BNODE_x1: $i, BNODE_x2: $i, BNODE_l1: $i, BNODE_l2: $i] : (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1) & iext(uri_owl_oneOf, BNODE_x1, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2) & iext(uri_owl_oneOf, BNODE_x2, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, uri_ex_u) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.50 tff(7,plain,(
% 0.19/0.50 iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7) & iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5) & iext(uri_rdf_first, BNODE_l1!5, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1!5, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2!6) & iext(uri_owl_oneOf, BNODE_x2!6, BNODE_l2!4) & iext(uri_rdf_first, BNODE_l2!4, uri_ex_u) & iext(uri_rdf_rest, BNODE_l2!4, uri_rdf_nil)),
% 0.19/0.50 inference(skolemize,[status(sab)],[6])).
% 0.19/0.50 tff(8,plain,
% 0.19/0.50 (iext(uri_rdf_rest, BNODE_l1!5, uri_rdf_nil)),
% 0.19/0.50 inference(and_elim,[status(thm)],[7])).
% 0.19/0.50 tff(9,plain,
% 0.19/0.50 (iext(uri_rdf_first, BNODE_l1!5, uri_ex_w)),
% 0.19/0.50 inference(and_elim,[status(thm)],[7])).
% 0.19/0.50 tff(10,plain,
% 0.19/0.50 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(11,plain,
% 0.19/0.50 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.50 tff(12,plain,
% 0.19/0.50 (^[Z: $i, S1: $i, A1: $i] : refl(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(13,plain,
% 0.19/0.50 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.50 tff(14,plain,
% 0.19/0.50 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(15,plain,
% 0.19/0.50 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.51 tff(16,plain,
% 0.19/0.51 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[15, 13])).
% 0.19/0.51 tff(17,plain,
% 0.19/0.51 (^[Z: $i, S1: $i, A1: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) <=> ((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))), trans(monotonicity(rewrite((~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))) <=> (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))), rewrite((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) <=> (((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))), rewrite((((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))) <=> (((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))))), rewrite((((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(18,plain,
% 0.19/0.51 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.51 tff(19,plain,
% 0.19/0.51 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(20,plain,
% 0.19/0.51 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.51 tff(21,plain,
% 0.19/0.51 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(22,plain,
% 0.19/0.51 (^[Z: $i, S1: $i, A1: $i] : trans(monotonicity(monotonicity(rewrite((ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))), ((iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), (((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), (((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(23,plain,
% 0.19/0.51 (![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.51 tff(24,axiom,(![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_enum_class_001')).
% 0.19/0.51 tff(25,plain,
% 0.19/0.51 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.51 tff(26,plain,
% 0.19/0.51 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.51 tff(27,plain,(
% 0.19/0.51 ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[26])).
% 0.19/0.51 tff(28,plain,
% 0.19/0.51 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.51 tff(29,plain,
% 0.19/0.51 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.51 tff(30,plain,
% 0.19/0.51 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.19/0.51 tff(31,plain,
% 0.19/0.51 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[30, 11])).
% 0.19/0.51 tff(32,plain,
% 0.19/0.51 (((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!5, uri_ex_w)) | (~iext(uri_rdf_rest, BNODE_l1!5, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5) | (~ic(BNODE_x1!7)) | (~(icext(BNODE_x1!7, tptp_fun_X_0(uri_ex_w, BNODE_x1!7)) <=> (tptp_fun_X_0(uri_ex_w, BNODE_x1!7) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5)) | (~((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, BNODE_l1!5, uri_ex_w)) | (~iext(uri_rdf_rest, BNODE_l1!5, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5) | (~ic(BNODE_x1!7)) | (~(icext(BNODE_x1!7, tptp_fun_X_0(uri_ex_w, BNODE_x1!7)) <=> (tptp_fun_X_0(uri_ex_w, BNODE_x1!7) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5)) | (~((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w))))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(33,plain,
% 0.19/0.51 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!5, uri_ex_w)) | (~iext(uri_rdf_rest, BNODE_l1!5, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5) | (~ic(BNODE_x1!7)) | (~(icext(BNODE_x1!7, tptp_fun_X_0(uri_ex_w, BNODE_x1!7)) <=> (tptp_fun_X_0(uri_ex_w, BNODE_x1!7) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5)) | (~((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w))))))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(34,plain,
% 0.19/0.51 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, BNODE_l1!5, uri_ex_w)) | (~iext(uri_rdf_rest, BNODE_l1!5, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5) | (~ic(BNODE_x1!7)) | (~(icext(BNODE_x1!7, tptp_fun_X_0(uri_ex_w, BNODE_x1!7)) <=> (tptp_fun_X_0(uri_ex_w, BNODE_x1!7) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5)) | (~((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w)))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.51 tff(35,plain,
% 0.19/0.51 (~((~(iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5) | (~ic(BNODE_x1!7)) | (~(icext(BNODE_x1!7, tptp_fun_X_0(uri_ex_w, BNODE_x1!7)) <=> (tptp_fun_X_0(uri_ex_w, BNODE_x1!7) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5)) | (~((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w))))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[34, 31, 9, 8])).
% 0.19/0.51 tff(36,plain,
% 0.19/0.51 (((~(iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5) | (~ic(BNODE_x1!7)) | (~(icext(BNODE_x1!7, tptp_fun_X_0(uri_ex_w, BNODE_x1!7)) <=> (tptp_fun_X_0(uri_ex_w, BNODE_x1!7) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5)) | (~((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w)))))))) | ((~iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5)) | (~((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w))))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(37,plain,
% 0.19/0.51 ((~iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5)) | (~((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.51 tff(38,plain,
% 0.19/0.51 (iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5)),
% 0.19/0.51 inference(and_elim,[status(thm)],[7])).
% 0.19/0.51 tff(39,plain,
% 0.19/0.51 ((~((~iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5)) | (~((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w))))))) | (~iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5)) | (~((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w)))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(40,plain,
% 0.19/0.51 ((~((~iext(uri_owl_oneOf, BNODE_x1!7, BNODE_l1!5)) | (~((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w))))))) | (~((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.51 tff(41,plain,
% 0.19/0.51 (~((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.19/0.51 tff(42,plain,
% 0.19/0.51 (((~ic(BNODE_x1!7)) | (~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w)))) | ![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(43,plain,
% 0.19/0.51 (![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.51 tff(44,plain,
% 0.19/0.51 ((~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w))) | (icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p)) <=> (tptp_fun_X2_2(uri_ex_p) = uri_ex_w))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(45,plain,
% 0.19/0.51 (icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p)) <=> (tptp_fun_X2_2(uri_ex_p) = uri_ex_w)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.51 tff(46,plain,
% 0.19/0.51 (^[P: $i] : refl((iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P)) <=> (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(47,plain,
% 0.19/0.51 (![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P)) <=> ![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.51 tff(48,plain,
% 0.19/0.51 (![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P)) <=> ![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(49,axiom,(![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rdf_type_ip')).
% 0.19/0.51 tff(50,plain,
% 0.19/0.51 (![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.51 tff(51,plain,(
% 0.19/0.51 ![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))),
% 0.19/0.51 inference(skolemize,[status(sab)],[50])).
% 0.19/0.51 tff(52,plain,
% 0.19/0.51 (![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.51 tff(53,plain,
% 0.19/0.51 ((~![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))) | (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) <=> ip(uri_ex_p))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(54,plain,
% 0.19/0.51 (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) <=> ip(uri_ex_p)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.51 tff(55,plain,
% 0.19/0.51 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(56,plain,
% 0.19/0.51 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.51 tff(57,plain,
% 0.19/0.51 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(58,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rdfs_cext_def')).
% 0.19/0.51 tff(59,plain,
% 0.19/0.51 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.51 tff(60,plain,(
% 0.19/0.51 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.51 inference(skolemize,[status(sab)],[59])).
% 0.19/0.51 tff(61,plain,
% 0.19/0.51 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.19/0.51 tff(62,plain,
% 0.19/0.51 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) <=> icext(uri_rdf_Property, uri_ex_p))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(63,plain,
% 0.19/0.51 (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) <=> icext(uri_rdf_Property, uri_ex_p)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.19/0.51 tff(64,plain,
% 0.19/0.51 (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)),
% 0.19/0.51 inference(and_elim,[status(thm)],[7])).
% 0.19/0.51 tff(65,plain,
% 0.19/0.51 (iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property) <=> iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(66,axiom,(iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rdfs_domain_domain')).
% 0.19/0.51 tff(67,plain,
% 0.19/0.51 (iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.51 tff(68,plain,
% 0.19/0.51 (^[P: $i, C: $i, X: $i, Y: $i] : refl((icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))) <=> (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(69,plain,
% 0.19/0.51 (![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))) <=> ![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.51 tff(70,plain,
% 0.19/0.51 (^[P: $i, C: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) <=> (~((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))), ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) <=> (~(~((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))))), rewrite((~(~((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))) <=> ((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))), ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) <=> ((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))), (((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> (((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))) | icext(C, X)))), rewrite((((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))) | icext(C, X)) <=> (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))), (((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(71,plain,
% 0.19/0.51 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> ![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.51 tff(72,plain,
% 0.19/0.51 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> ![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(73,plain,
% 0.19/0.51 (^[P: $i, C: $i, X: $i, Y: $i] : rewrite(((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) => icext(C, X)) <=> ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(74,plain,
% 0.19/0.51 (![P: $i, C: $i, X: $i, Y: $i] : ((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) => icext(C, X)) <=> ![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.51 tff(75,axiom,(![P: $i, C: $i, X: $i, Y: $i] : ((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) => icext(C, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rdfs_domain_main')).
% 0.19/0.51 tff(76,plain,
% 0.19/0.51 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.51 tff(77,plain,
% 0.19/0.51 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.19/0.51 tff(78,plain,(
% 0.19/0.51 ![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.19/0.51 inference(skolemize,[status(sab)],[77])).
% 0.19/0.51 tff(79,plain,
% 0.19/0.51 (![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.19/0.51 tff(80,plain,
% 0.19/0.51 (![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[79, 69])).
% 0.19/0.51 tff(81,plain,
% 0.19/0.51 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | ((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(uri_rdf_Property, uri_ex_p) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(uri_rdf_Property, uri_ex_p) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(82,plain,
% 0.19/0.51 ((icext(uri_rdf_Property, uri_ex_p) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7))) <=> ((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(uri_rdf_Property, uri_ex_p) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(83,plain,
% 0.19/0.51 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (icext(uri_rdf_Property, uri_ex_p) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | ((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(uri_rdf_Property, uri_ex_p) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.51 tff(84,plain,
% 0.19/0.51 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (icext(uri_rdf_Property, uri_ex_p) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(uri_rdf_Property, uri_ex_p) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)))),
% 0.19/0.52 inference(transitivity,[status(thm)],[83, 81])).
% 0.19/0.52 tff(85,plain,
% 0.19/0.52 ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (icext(uri_rdf_Property, uri_ex_p) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(86,plain,
% 0.19/0.52 ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(uri_rdf_Property, uri_ex_p) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.52 tff(87,plain,
% 0.19/0.52 (icext(uri_rdf_Property, uri_ex_p)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[86, 80, 67, 64])).
% 0.19/0.52 tff(88,plain,
% 0.19/0.52 ((~(iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) <=> icext(uri_rdf_Property, uri_ex_p))) | iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) | (~icext(uri_rdf_Property, uri_ex_p))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(89,plain,
% 0.19/0.52 ((~(iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) <=> icext(uri_rdf_Property, uri_ex_p))) | iext(uri_rdf_type, uri_ex_p, uri_rdf_Property)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.19/0.52 tff(90,plain,
% 0.19/0.52 (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[89, 63])).
% 0.19/0.52 tff(91,plain,
% 0.19/0.52 ((~(iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) <=> ip(uri_ex_p))) | (~iext(uri_rdf_type, uri_ex_p, uri_rdf_Property)) | ip(uri_ex_p)),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(92,plain,
% 0.19/0.52 ((~(iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) <=> ip(uri_ex_p))) | ip(uri_ex_p)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.52 tff(93,plain,
% 0.19/0.52 (ip(uri_ex_p)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[92, 54])).
% 0.19/0.52 tff(94,plain,
% 0.19/0.52 (^[P: $i] : rewrite((~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))))) <=> (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(95,plain,
% 0.19/0.52 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))))) <=> ![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.52 tff(96,plain,
% 0.19/0.52 (^[P: $i] : refl((~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(97,plain,
% 0.19/0.52 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.52 tff(98,plain,
% 0.19/0.52 (^[P: $i] : rewrite((~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(99,plain,
% 0.19/0.52 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.52 tff(100,plain,
% 0.19/0.52 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[99, 97])).
% 0.19/0.52 tff(101,plain,
% 0.19/0.52 (^[P: $i] : trans(monotonicity(rewrite(((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) <=> ((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))), trans(monotonicity(rewrite((~((~(iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P)) & iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))) | (tptp_fun_X1_3(P) = tptp_fun_X2_2(P)))) <=> (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))))), ((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P)) & iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))) | (tptp_fun_X1_3(P) = tptp_fun_X2_2(P))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))))))), rewrite((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))), ((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P)) & iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))) | (tptp_fun_X1_3(P) = tptp_fun_X2_2(P))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))))))), ((((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P)) & iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))) | (tptp_fun_X1_3(P) = tptp_fun_X2_2(P)))))) <=> (((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))))), rewrite((((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))))))))), ((((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P)) & iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))) | (tptp_fun_X1_3(P) = tptp_fun_X2_2(P)))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(102,plain,
% 0.19/0.52 (![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P)) & iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))) | (tptp_fun_X1_3(P) = tptp_fun_X2_2(P)))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[101])).
% 0.19/0.52 tff(103,plain,
% 0.19/0.52 (^[P: $i] : rewrite((((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P)) & iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))) | (tptp_fun_X1_3(P) = tptp_fun_X2_2(P))))))) <=> (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P)) & iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))) | (tptp_fun_X1_3(P) = tptp_fun_X2_2(P)))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(104,plain,
% 0.19/0.52 (![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P)) & iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))) | (tptp_fun_X1_3(P) = tptp_fun_X2_2(P))))))) <=> ![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P)) & iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))) | (tptp_fun_X1_3(P) = tptp_fun_X2_2(P))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[103])).
% 0.19/0.52 tff(105,plain,
% 0.19/0.52 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) <=> ![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(106,plain,
% 0.19/0.52 (^[P: $i] : rewrite((icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((iext(P, X1, Y) & iext(P, X2, Y)) => (X1 = X2)))) <=> (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(107,plain,
% 0.19/0.52 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((iext(P, X1, Y) & iext(P, X2, Y)) => (X1 = X2)))) <=> ![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.52 tff(108,axiom,(![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((iext(P, X1, Y) & iext(P, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_char_inversefunctional')).
% 0.19/0.52 tff(109,plain,
% 0.19/0.52 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.52 tff(110,plain,
% 0.19/0.52 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.19/0.52 tff(111,plain,(
% 0.19/0.52 ![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P)) & iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))) | (tptp_fun_X1_3(P) = tptp_fun_X2_2(P)))))))),
% 0.19/0.52 inference(skolemize,[status(sab)],[110])).
% 0.19/0.52 tff(112,plain,
% 0.19/0.52 (![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P)) & iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))) | (tptp_fun_X1_3(P) = tptp_fun_X2_2(P))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.19/0.52 tff(113,plain,
% 0.19/0.52 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[112, 102])).
% 0.19/0.52 tff(114,plain,
% 0.19/0.52 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P)))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[113, 100])).
% 0.19/0.52 tff(115,plain,
% 0.19/0.52 (![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[114, 95])).
% 0.19/0.52 tff(116,plain,
% 0.19/0.52 (((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(117,plain,
% 0.19/0.52 ((~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))) <=> (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(118,plain,
% 0.19/0.52 (((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.52 tff(119,plain,
% 0.19/0.52 (((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[118, 116])).
% 0.19/0.52 tff(120,plain,
% 0.19/0.52 ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(121,plain,
% 0.19/0.52 ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_3(P) = tptp_fun_X2_2(P)) | (~iext(P, tptp_fun_X1_3(P), tptp_fun_Y_1(P))) | (~iext(P, tptp_fun_X2_2(P), tptp_fun_Y_1(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.52 tff(122,plain,
% 0.19/0.52 (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[121, 115])).
% 0.19/0.52 tff(123,plain,
% 0.19/0.52 (((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))) | (icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(124,plain,
% 0.19/0.52 (icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.19/0.52 tff(125,plain,
% 0.19/0.52 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(126,plain,
% 0.19/0.52 (iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[125, 61])).
% 0.19/0.52 tff(127,plain,
% 0.19/0.52 ((~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)) <=> (~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(128,axiom,(~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_conclusion_fullish_026_Inferred_Property_Characteristics_I')).
% 0.19/0.52 tff(129,plain,
% 0.19/0.52 (~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.52 tff(130,plain,
% 0.19/0.52 ((~(iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))) | iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) | (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(131,plain,
% 0.19/0.52 ((~(iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))) | (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.19/0.52 tff(132,plain,
% 0.19/0.52 (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[131, 126])).
% 0.19/0.52 tff(133,plain,
% 0.19/0.52 ((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)))))) | icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(134,plain,
% 0.19/0.52 ((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)))))) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.19/0.52 tff(135,plain,
% 0.19/0.52 ((~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[134, 124])).
% 0.19/0.52 tff(136,plain,
% 0.19/0.52 (~((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[135, 93])).
% 0.19/0.52 tff(137,plain,
% 0.19/0.52 (((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p))) | iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(138,plain,
% 0.19/0.52 (iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.19/0.52 tff(139,plain,
% 0.19/0.52 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | ((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p)))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(140,plain,
% 0.19/0.52 ((icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p)) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | (~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p)))) <=> ((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(141,plain,
% 0.19/0.53 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p)) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | (~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | ((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[140])).
% 0.19/0.53 tff(142,plain,
% 0.19/0.53 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p)) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | (~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p)))),
% 0.19/0.53 inference(transitivity,[status(thm)],[141, 139])).
% 0.19/0.53 tff(143,plain,
% 0.19/0.53 ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p)) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | (~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(144,plain,
% 0.19/0.53 ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.19/0.53 tff(145,plain,
% 0.19/0.53 (icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[144, 80, 64, 138])).
% 0.19/0.53 tff(146,plain,
% 0.19/0.53 ((~(icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p)) <=> (tptp_fun_X2_2(uri_ex_p) = uri_ex_w))) | (~icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p))) | (tptp_fun_X2_2(uri_ex_p) = uri_ex_w)),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(147,plain,
% 0.19/0.53 ((~(icext(BNODE_x1!7, tptp_fun_X2_2(uri_ex_p)) <=> (tptp_fun_X2_2(uri_ex_p) = uri_ex_w))) | (tptp_fun_X2_2(uri_ex_p) = uri_ex_w)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.19/0.53 tff(148,plain,
% 0.19/0.53 (tptp_fun_X2_2(uri_ex_p) = uri_ex_w),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[147, 45])).
% 0.19/0.53 tff(149,plain,
% 0.19/0.53 (uri_ex_w = tptp_fun_X2_2(uri_ex_p)),
% 0.19/0.53 inference(symmetry,[status(thm)],[148])).
% 0.19/0.53 tff(150,plain,
% 0.19/0.53 ((~![X: $i] : (icext(BNODE_x1!7, X) <=> (X = uri_ex_w))) | (icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p)) <=> (tptp_fun_X1_3(uri_ex_p) = uri_ex_w))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(151,plain,
% 0.19/0.53 (icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p)) <=> (tptp_fun_X1_3(uri_ex_p) = uri_ex_w)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[150, 43])).
% 0.19/0.53 tff(152,plain,
% 0.19/0.53 (((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p))) | iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(153,plain,
% 0.19/0.53 (iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[152, 136])).
% 0.19/0.53 tff(154,plain,
% 0.19/0.53 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | ((~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p)))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(155,plain,
% 0.19/0.53 ((icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p)) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p)))) <=> ((~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(156,plain,
% 0.19/0.53 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p)) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | ((~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[155])).
% 0.19/0.53 tff(157,plain,
% 0.19/0.53 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p)) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p)))),
% 0.19/0.53 inference(transitivity,[status(thm)],[156, 154])).
% 0.19/0.53 tff(158,plain,
% 0.19/0.53 ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p)) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(159,plain,
% 0.19/0.53 ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!7)) | icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.53 tff(160,plain,
% 0.19/0.53 ((~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[159, 80, 64])).
% 0.19/0.53 tff(161,plain,
% 0.19/0.53 (icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[160, 153])).
% 0.19/0.53 tff(162,plain,
% 0.19/0.53 ((~(icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p)) <=> (tptp_fun_X1_3(uri_ex_p) = uri_ex_w))) | (~icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = uri_ex_w)),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(163,plain,
% 0.19/0.53 ((~(icext(BNODE_x1!7, tptp_fun_X1_3(uri_ex_p)) <=> (tptp_fun_X1_3(uri_ex_p) = uri_ex_w))) | (tptp_fun_X1_3(uri_ex_p) = uri_ex_w)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.19/0.53 tff(164,plain,
% 0.19/0.53 (tptp_fun_X1_3(uri_ex_p) = uri_ex_w),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[163, 151])).
% 0.19/0.53 tff(165,plain,
% 0.19/0.53 (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)),
% 0.19/0.53 inference(transitivity,[status(thm)],[164, 149])).
% 0.19/0.53 tff(166,plain,
% 0.19/0.53 (((~iext(uri_ex_p, tptp_fun_X2_2(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_3(uri_ex_p), tptp_fun_Y_1(uri_ex_p))) | (tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p))) | (~(tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p)))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(167,plain,
% 0.19/0.53 (~(tptp_fun_X1_3(uri_ex_p) = tptp_fun_X2_2(uri_ex_p))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[166, 136])).
% 0.19/0.53 tff(168,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[167, 165])).
% 0.19/0.53 % SZS output end Proof
% 0.19/0.53 % E exiting
%------------------------------------------------------------------------------