%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB026+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.62s 0.79s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SWB026+1 : TPTP v9.0.0. Released v5.2.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 07:52:32 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.62/0.79 % SZS status Theorem
% 0.62/0.79 % SZS output start Proof
% 0.62/0.79 tff(tptp_fun_X2_115_type, type, (
% 0.62/0.79 tptp_fun_X2_115: $i > $i)).
% 0.62/0.79 tff(uri_ex_p_type, type, (
% 0.62/0.79 uri_ex_p: $i)).
% 0.62/0.79 tff(tptp_fun_X1_116_type, type, (
% 0.62/0.79 tptp_fun_X1_116: $i > $i)).
% 0.62/0.79 tff(uri_ex_w_type, type, (
% 0.62/0.79 uri_ex_w: $i)).
% 0.62/0.79 tff(icext_type, type, (
% 0.62/0.79 icext: ( $i * $i ) > $o)).
% 0.62/0.79 tff(tptp_fun_BNODE_x1_143_type, type, (
% 0.62/0.79 tptp_fun_BNODE_x1_143: $i)).
% 0.62/0.79 tff(ic_type, type, (
% 0.62/0.79 ic: $i > $o)).
% 0.62/0.79 tff(iext_type, type, (
% 0.62/0.79 iext: ( $i * $i * $i ) > $o)).
% 0.62/0.79 tff(tptp_fun_BNODE_l1_141_type, type, (
% 0.62/0.79 tptp_fun_BNODE_l1_141: $i)).
% 0.62/0.79 tff(uri_owl_oneOf_type, type, (
% 0.62/0.79 uri_owl_oneOf: $i)).
% 0.62/0.79 tff(tptp_fun_X_8_type, type, (
% 0.62/0.79 tptp_fun_X_8: ( $i * $i ) > $i)).
% 0.62/0.79 tff(uri_rdf_nil_type, type, (
% 0.62/0.79 uri_rdf_nil: $i)).
% 0.62/0.79 tff(uri_rdf_rest_type, type, (
% 0.62/0.79 uri_rdf_rest: $i)).
% 0.62/0.79 tff(tptp_fun_BNODE_l2_140_type, type, (
% 0.62/0.79 tptp_fun_BNODE_l2_140: $i)).
% 0.62/0.79 tff(uri_ex_u_type, type, (
% 0.62/0.79 uri_ex_u: $i)).
% 0.62/0.79 tff(uri_rdf_first_type, type, (
% 0.62/0.79 uri_rdf_first: $i)).
% 0.62/0.79 tff(tptp_fun_BNODE_x2_142_type, type, (
% 0.62/0.79 tptp_fun_BNODE_x2_142: $i)).
% 0.62/0.79 tff(uri_rdfs_range_type, type, (
% 0.62/0.79 uri_rdfs_range: $i)).
% 0.62/0.79 tff(uri_rdfs_domain_type, type, (
% 0.62/0.79 uri_rdfs_domain: $i)).
% 0.62/0.79 tff(tptp_fun_Y_114_type, type, (
% 0.62/0.79 tptp_fun_Y_114: $i > $i)).
% 0.62/0.79 tff(ip_type, type, (
% 0.62/0.79 ip: $i > $o)).
% 0.62/0.79 tff(uri_owl_InverseFunctionalProperty_type, type, (
% 0.62/0.79 uri_owl_InverseFunctionalProperty: $i)).
% 0.62/0.79 tff(tptp_fun_X_58_type, type, (
% 0.62/0.79 tptp_fun_X_58: ( $i * $i ) > $i)).
% 0.62/0.79 tff(tptp_fun_Y_57_type, type, (
% 0.62/0.79 tptp_fun_Y_57: ( $i * $i ) > $i)).
% 0.62/0.79 tff(uri_rdf_type_type, type, (
% 0.62/0.79 uri_rdf_type: $i)).
% 0.62/0.79 tff(1,plain,
% 0.62/0.79 ((uri_ex_w = tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_w)),
% 0.62/0.79 inference(commutativity,[status(thm)],[])).
% 0.62/0.79 tff(2,plain,
% 0.62/0.79 (?[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))),
% 0.62/0.79 inference(rewrite,[status(thm)],[])).
% 0.62/0.79 tff(3,plain,
% 0.62/0.79 (^[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))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(4,plain,
% 0.62/0.79 (?[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))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[3])).
% 0.62/0.79 tff(5,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')).
% 0.62/0.79 tff(6,plain,
% 0.62/0.79 (?[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))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.62/0.79 tff(7,plain,
% 0.62/0.79 (?[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))),
% 0.62/0.79 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.62/0.79 tff(8,plain,(
% 0.62/0.79 iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143) & iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141) & iext(uri_rdf_first, BNODE_l1!141, uri_ex_w) & iext(uri_rdf_rest, BNODE_l1!141, uri_rdf_nil) & iext(uri_rdfs_range, uri_ex_p, BNODE_x2!142) & iext(uri_owl_oneOf, BNODE_x2!142, BNODE_l2!140) & iext(uri_rdf_first, BNODE_l2!140, uri_ex_u) & iext(uri_rdf_rest, BNODE_l2!140, uri_rdf_nil)),
% 0.62/0.79 inference(skolemize,[status(sab)],[7])).
% 0.62/0.79 tff(9,plain,
% 0.62/0.79 (iext(uri_rdf_rest, BNODE_l1!141, uri_rdf_nil)),
% 0.62/0.79 inference(and_elim,[status(thm)],[8])).
% 0.62/0.79 tff(10,plain,
% 0.62/0.79 (iext(uri_rdf_first, BNODE_l1!141, uri_ex_w)),
% 0.62/0.79 inference(and_elim,[status(thm)],[8])).
% 0.62/0.79 tff(11,plain,
% 0.62/0.79 (^[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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))))))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(12,plain,
% 0.62/0.79 (![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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[11])).
% 0.62/0.79 tff(13,plain,
% 0.62/0.79 (^[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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(14,plain,
% 0.62/0.79 (![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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[13])).
% 0.62/0.79 tff(15,plain,
% 0.62/0.79 (^[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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(16,plain,
% 0.62/0.79 (![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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[15])).
% 0.62/0.79 tff(17,plain,
% 0.62/0.79 (![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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.62/0.79 inference(transitivity,[status(thm)],[16, 14])).
% 0.62/0.79 tff(18,plain,
% 0.62/0.79 (^[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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))) <=> (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))), rewrite((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))))),
% 0.62/0.79 inference(bind,[status(th)],[])).
% 0.62/0.79 tff(19,plain,
% 0.62/0.79 (![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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.62/0.79 inference(quant_intro,[status(thm)],[18])).
% 0.62/0.79 tff(20,plain,
% 0.62/0.79 (^[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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(21,plain,
% 0.62/0.80 (![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_8(A1, Z)) <=> (tptp_fun_X_8(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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[20])).
% 0.62/0.80 tff(22,plain,
% 0.62/0.80 (![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)))))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(23,plain,
% 0.62/0.80 (^[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)))))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(24,plain,
% 0.62/0.80 (![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)))))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[23])).
% 0.62/0.80 tff(25,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/Axioms/SWB001+0.ax','owl_enum_class_001')).
% 0.62/0.80 tff(26,plain,
% 0.62/0.80 (![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)))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.62/0.80 tff(27,plain,
% 0.62/0.80 (![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)))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.62/0.80 tff(28,plain,(
% 0.62/0.80 ![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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.62/0.80 inference(skolemize,[status(sab)],[27])).
% 0.62/0.80 tff(29,plain,
% 0.62/0.80 (![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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.62/0.80 tff(30,plain,
% 0.62/0.80 (![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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.62/0.80 tff(31,plain,
% 0.62/0.80 (![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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[30, 17])).
% 0.62/0.80 tff(32,plain,
% 0.62/0.80 (![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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[31, 12])).
% 0.62/0.80 tff(33,plain,
% 0.62/0.80 (((~![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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!141, uri_ex_w)) | (~iext(uri_rdf_rest, BNODE_l1!141, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141) | (~ic(BNODE_x1!143)) | (~(icext(BNODE_x1!143, tptp_fun_X_8(uri_ex_w, BNODE_x1!143)) <=> (tptp_fun_X_8(uri_ex_w, BNODE_x1!143) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141)) | (~((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, 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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, BNODE_l1!141, uri_ex_w)) | (~iext(uri_rdf_rest, BNODE_l1!141, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141) | (~ic(BNODE_x1!143)) | (~(icext(BNODE_x1!143, tptp_fun_X_8(uri_ex_w, BNODE_x1!143)) <=> (tptp_fun_X_8(uri_ex_w, BNODE_x1!143) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141)) | (~((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w))))))))))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(34,plain,
% 0.62/0.80 ((~![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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!141, uri_ex_w)) | (~iext(uri_rdf_rest, BNODE_l1!141, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141) | (~ic(BNODE_x1!143)) | (~(icext(BNODE_x1!143, tptp_fun_X_8(uri_ex_w, BNODE_x1!143)) <=> (tptp_fun_X_8(uri_ex_w, BNODE_x1!143) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141)) | (~((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w))))))))))),
% 0.62/0.80 inference(quant_inst,[status(thm)],[])).
% 0.62/0.80 tff(35,plain,
% 0.62/0.80 ((~![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_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, BNODE_l1!141, uri_ex_w)) | (~iext(uri_rdf_rest, BNODE_l1!141, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141) | (~ic(BNODE_x1!143)) | (~(icext(BNODE_x1!143, tptp_fun_X_8(uri_ex_w, BNODE_x1!143)) <=> (tptp_fun_X_8(uri_ex_w, BNODE_x1!143) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141)) | (~((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w)))))))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.62/0.80 tff(36,plain,
% 0.62/0.80 (~((~(iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141) | (~ic(BNODE_x1!143)) | (~(icext(BNODE_x1!143, tptp_fun_X_8(uri_ex_w, BNODE_x1!143)) <=> (tptp_fun_X_8(uri_ex_w, BNODE_x1!143) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141)) | (~((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w))))))))),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[35, 32, 10, 9])).
% 0.62/0.80 tff(37,plain,
% 0.62/0.80 (((~(iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141) | (~ic(BNODE_x1!143)) | (~(icext(BNODE_x1!143, tptp_fun_X_8(uri_ex_w, BNODE_x1!143)) <=> (tptp_fun_X_8(uri_ex_w, BNODE_x1!143) = uri_ex_w))))) | (~((~iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141)) | (~((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w)))))))) | ((~iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141)) | (~((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w))))))),
% 0.62/0.80 inference(tautology,[status(thm)],[])).
% 0.62/0.80 tff(38,plain,
% 0.62/0.80 ((~iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141)) | (~((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w)))))),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.62/0.80 tff(39,plain,
% 0.62/0.80 (iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141)),
% 0.62/0.80 inference(and_elim,[status(thm)],[8])).
% 0.62/0.80 tff(40,plain,
% 0.62/0.80 ((~((~iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141)) | (~((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w))))))) | (~iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141)) | (~((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w)))))),
% 0.62/0.80 inference(tautology,[status(thm)],[])).
% 0.62/0.80 tff(41,plain,
% 0.62/0.80 ((~((~iext(uri_owl_oneOf, BNODE_x1!143, BNODE_l1!141)) | (~((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w))))))) | (~((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w)))))),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.62/0.80 tff(42,plain,
% 0.62/0.80 (~((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w))))),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.62/0.80 tff(43,plain,
% 0.62/0.80 (((~ic(BNODE_x1!143)) | (~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w)))) | ![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w))),
% 0.62/0.80 inference(tautology,[status(thm)],[])).
% 0.62/0.80 tff(44,plain,
% 0.62/0.80 (![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w))),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.62/0.80 tff(45,plain,
% 0.62/0.80 ((~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w))) | (icext(BNODE_x1!143, tptp_fun_X1_116(uri_ex_p)) <=> (tptp_fun_X1_116(uri_ex_p) = uri_ex_w))),
% 0.62/0.80 inference(quant_inst,[status(thm)],[])).
% 0.62/0.80 tff(46,plain,
% 0.62/0.80 (icext(BNODE_x1!143, tptp_fun_X1_116(uri_ex_p)) <=> (tptp_fun_X1_116(uri_ex_p) = uri_ex_w)),
% 0.62/0.80 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.62/0.80 tff(47,plain,
% 0.62/0.80 (^[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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))) <=> (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(48,plain,
% 0.62/0.80 (![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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))) <=> ![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[47])).
% 0.62/0.80 tff(49,plain,
% 0.62/0.80 (^[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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(50,plain,
% 0.62/0.80 (![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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[49])).
% 0.62/0.80 tff(51,plain,
% 0.62/0.80 (^[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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(52,plain,
% 0.62/0.80 (![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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[51])).
% 0.62/0.80 tff(53,plain,
% 0.62/0.80 (![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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 0.62/0.80 inference(transitivity,[status(thm)],[52, 50])).
% 0.62/0.80 tff(54,plain,
% 0.62/0.80 (^[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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P)))) <=> (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))), ((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))), rewrite((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))), ((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(55,plain,
% 0.62/0.80 (![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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[54])).
% 0.62/0.80 tff(56,plain,
% 0.62/0.80 (^[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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P)))))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(57,plain,
% 0.62/0.80 (![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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[56])).
% 0.62/0.80 tff(58,plain,
% 0.62/0.80 (![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))))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(59,plain,
% 0.62/0.80 (^[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)))))),
% 0.62/0.80 inference(bind,[status(th)],[])).
% 0.62/0.80 tff(60,plain,
% 0.62/0.80 (![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))))),
% 0.62/0.80 inference(quant_intro,[status(thm)],[59])).
% 0.62/0.80 tff(61,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/Axioms/SWB001+0.ax','owl_char_inversefunctional')).
% 0.62/0.80 tff(62,plain,
% 0.62/0.80 (![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))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.62/0.80 tff(63,plain,
% 0.62/0.80 (![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))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.62/0.80 tff(64,plain,(
% 0.62/0.80 ![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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P)))))))),
% 0.62/0.80 inference(skolemize,[status(sab)],[63])).
% 0.62/0.80 tff(65,plain,
% 0.62/0.80 (![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_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.62/0.80 tff(66,plain,
% 0.62/0.80 (![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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.62/0.80 tff(67,plain,
% 0.62/0.80 (![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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[66, 53])).
% 0.62/0.80 tff(68,plain,
% 0.62/0.80 (![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))),
% 0.62/0.80 inference(modus_ponens,[status(thm)],[67, 48])).
% 0.62/0.80 tff(69,plain,
% 0.62/0.80 (((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(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)))))))))))),
% 0.62/0.80 inference(rewrite,[status(thm)],[])).
% 0.62/0.80 tff(70,plain,
% 0.62/0.80 ((~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(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_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(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))))))))))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(71,plain,
% 0.62/0.81 (((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(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)))))))))))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[70])).
% 0.62/0.81 tff(72,plain,
% 0.62/0.81 (((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(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_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(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)))))))))))),
% 0.62/0.81 inference(transitivity,[status(thm)],[71, 69])).
% 0.62/0.81 tff(73,plain,
% 0.62/0.81 ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(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))))))))))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(74,plain,
% 0.62/0.81 ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(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_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(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))))))))))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.62/0.81 tff(75,plain,
% 0.62/0.81 (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(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)))))))))),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[74, 68])).
% 0.62/0.81 tff(76,plain,
% 0.62/0.81 (((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(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_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))),
% 0.62/0.81 inference(tautology,[status(thm)],[])).
% 0.62/0.81 tff(77,plain,
% 0.62/0.81 (icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))))),
% 0.62/0.81 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.62/0.81 tff(78,plain,
% 0.62/0.81 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(79,plain,
% 0.62/0.81 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[78])).
% 0.62/0.81 tff(80,plain,
% 0.62/0.81 (^[P: $i, C: $i] : refl((~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(81,plain,
% 0.62/0.81 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[80])).
% 0.62/0.81 tff(82,plain,
% 0.62/0.81 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(83,plain,
% 0.62/0.81 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[82])).
% 0.62/0.81 tff(84,plain,
% 0.62/0.81 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 0.62/0.81 inference(transitivity,[status(thm)],[83, 81])).
% 0.62/0.81 tff(85,plain,
% 0.62/0.81 (^[P: $i, C: $i] : trans(monotonicity(rewrite(((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) <=> ((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))), rewrite((iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))) <=> (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))), ((((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> (((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))), rewrite((((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))), ((((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(86,plain,
% 0.62/0.81 (![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[85])).
% 0.62/0.81 tff(87,plain,
% 0.62/0.81 (^[P: $i, C: $i] : rewrite((((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | ((~ip(P)) | (~ic(C)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))) <=> (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(88,plain,
% 0.62/0.81 (![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | ((~ip(P)) | (~ic(C)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))) <=> ![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[87])).
% 0.62/0.81 tff(89,plain,
% 0.62/0.81 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(90,plain,
% 0.62/0.81 (^[P: $i, C: $i] : rewrite((iext(uri_rdfs_domain, P, C) <=> ((ip(P) & ic(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, X)))) <=> (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))),
% 0.62/0.81 inference(bind,[status(th)],[])).
% 0.62/0.81 tff(91,plain,
% 0.62/0.81 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> ((ip(P) & ic(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, X)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 0.62/0.81 inference(quant_intro,[status(thm)],[90])).
% 0.62/0.81 tff(92,axiom,(![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> ((ip(P) & ic(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_rdfsext_domain')).
% 0.62/0.81 tff(93,plain,
% 0.62/0.81 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.62/0.81 tff(94,plain,
% 0.62/0.81 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.62/0.81 tff(95,plain,(
% 0.62/0.81 ![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | ((~ip(P)) | (~ic(C)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))),
% 0.62/0.81 inference(skolemize,[status(sab)],[94])).
% 0.62/0.81 tff(96,plain,
% 0.62/0.81 (![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.62/0.81 tff(97,plain,
% 0.62/0.81 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[96, 86])).
% 0.62/0.81 tff(98,plain,
% 0.62/0.81 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[97, 84])).
% 0.62/0.81 tff(99,plain,
% 0.62/0.81 (![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))),
% 0.62/0.81 inference(modus_ponens,[status(thm)],[98, 79])).
% 0.62/0.81 tff(100,plain,
% 0.62/0.81 (((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143) | (~ip(uri_ex_p)) | (~ic(BNODE_x1!143)) | (~((~iext(uri_ex_p, tptp_fun_X_58(BNODE_x1!143, uri_ex_p), tptp_fun_Y_57(BNODE_x1!143, uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X_58(BNODE_x1!143, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X)))))))))) <=> ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143) | (~ip(uri_ex_p)) | (~ic(BNODE_x1!143)) | (~((~iext(uri_ex_p, tptp_fun_X_58(BNODE_x1!143, uri_ex_p), tptp_fun_Y_57(BNODE_x1!143, uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X_58(BNODE_x1!143, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))))))))))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(101,plain,
% 0.62/0.81 ((~((~(iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143) | (~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X_58(BNODE_x1!143, uri_ex_p), tptp_fun_Y_57(BNODE_x1!143, uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X_58(BNODE_x1!143, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))))))))) <=> (~((~(iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143) | (~ip(uri_ex_p)) | (~ic(BNODE_x1!143)) | (~((~iext(uri_ex_p, tptp_fun_X_58(BNODE_x1!143, uri_ex_p), tptp_fun_Y_57(BNODE_x1!143, uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X_58(BNODE_x1!143, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X)))))))))),
% 0.62/0.81 inference(rewrite,[status(thm)],[])).
% 0.62/0.81 tff(102,plain,
% 0.62/0.81 (((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143) | (~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X_58(BNODE_x1!143, uri_ex_p), tptp_fun_Y_57(BNODE_x1!143, uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X_58(BNODE_x1!143, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X)))))))))) <=> ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143) | (~ip(uri_ex_p)) | (~ic(BNODE_x1!143)) | (~((~iext(uri_ex_p, tptp_fun_X_58(BNODE_x1!143, uri_ex_p), tptp_fun_Y_57(BNODE_x1!143, uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X_58(BNODE_x1!143, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))))))))))),
% 0.62/0.81 inference(monotonicity,[status(thm)],[101])).
% 0.62/0.81 tff(103,plain,
% 0.62/0.81 (((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143) | (~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X_58(BNODE_x1!143, uri_ex_p), tptp_fun_Y_57(BNODE_x1!143, uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X_58(BNODE_x1!143, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X)))))))))) <=> ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143) | (~ip(uri_ex_p)) | (~ic(BNODE_x1!143)) | (~((~iext(uri_ex_p, tptp_fun_X_58(BNODE_x1!143, uri_ex_p), tptp_fun_Y_57(BNODE_x1!143, uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X_58(BNODE_x1!143, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))))))))))),
% 0.62/0.81 inference(transitivity,[status(thm)],[102, 100])).
% 0.62/0.81 tff(104,plain,
% 0.62/0.81 ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143) | (~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X_58(BNODE_x1!143, uri_ex_p), tptp_fun_Y_57(BNODE_x1!143, uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X_58(BNODE_x1!143, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X)))))))))),
% 0.62/0.81 inference(quant_inst,[status(thm)],[])).
% 0.62/0.81 tff(105,plain,
% 0.62/0.81 ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143) | (~ip(uri_ex_p)) | (~ic(BNODE_x1!143)) | (~((~iext(uri_ex_p, tptp_fun_X_58(BNODE_x1!143, uri_ex_p), tptp_fun_Y_57(BNODE_x1!143, uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X_58(BNODE_x1!143, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X)))))))))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.62/0.82 tff(106,plain,
% 0.62/0.82 (~((~(iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143) | (~ip(uri_ex_p)) | (~ic(BNODE_x1!143)) | (~((~iext(uri_ex_p, tptp_fun_X_58(BNODE_x1!143, uri_ex_p), tptp_fun_Y_57(BNODE_x1!143, uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X_58(BNODE_x1!143, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))))))))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[105, 99])).
% 0.62/0.82 tff(107,plain,
% 0.62/0.82 (((~(iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143) | (~ip(uri_ex_p)) | (~ic(BNODE_x1!143)) | (~((~iext(uri_ex_p, tptp_fun_X_58(BNODE_x1!143, uri_ex_p), tptp_fun_Y_57(BNODE_x1!143, uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X_58(BNODE_x1!143, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X)))))))) | ((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))))))),
% 0.62/0.82 inference(tautology,[status(thm)],[])).
% 0.62/0.82 tff(108,plain,
% 0.62/0.82 ((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X)))))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.62/0.82 tff(109,plain,
% 0.62/0.82 (iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)),
% 0.62/0.82 inference(and_elim,[status(thm)],[8])).
% 0.62/0.82 tff(110,plain,
% 0.62/0.82 ((~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))))))) | (~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X)))))),
% 0.62/0.82 inference(tautology,[status(thm)],[])).
% 0.62/0.82 tff(111,plain,
% 0.62/0.82 ((~((~iext(uri_rdfs_domain, uri_ex_p, BNODE_x1!143)) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))))))) | (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X)))))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.62/0.82 tff(112,plain,
% 0.62/0.82 (~((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[111, 108])).
% 0.62/0.82 tff(113,plain,
% 0.62/0.82 (((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X)))) | ip(uri_ex_p)),
% 0.62/0.82 inference(tautology,[status(thm)],[])).
% 0.62/0.82 tff(114,plain,
% 0.62/0.82 (ip(uri_ex_p)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.62/0.82 tff(115,plain,
% 0.62/0.82 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.62/0.82 inference(bind,[status(th)],[])).
% 0.62/0.82 tff(116,plain,
% 0.62/0.82 (![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))),
% 0.62/0.82 inference(quant_intro,[status(thm)],[115])).
% 0.62/0.82 tff(117,plain,
% 0.62/0.82 (![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))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(118,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','rdfs_cext_def')).
% 0.62/0.82 tff(119,plain,
% 0.62/0.82 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.62/0.82 tff(120,plain,(
% 0.62/0.82 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.62/0.82 inference(skolemize,[status(sab)],[119])).
% 0.62/0.82 tff(121,plain,
% 0.62/0.82 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.62/0.82 tff(122,plain,
% 0.62/0.82 ((~![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))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(123,plain,
% 0.62/0.82 (iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.62/0.82 tff(124,plain,
% 0.62/0.82 ((~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)) <=> (~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(125,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')).
% 0.62/0.82 tff(126,plain,
% 0.62/0.82 (~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.62/0.82 tff(127,plain,
% 0.62/0.82 ((~(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))),
% 0.62/0.82 inference(tautology,[status(thm)],[])).
% 0.62/0.82 tff(128,plain,
% 0.62/0.82 ((~(iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))) | (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.62/0.82 tff(129,plain,
% 0.62/0.82 (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[128, 123])).
% 0.62/0.82 tff(130,plain,
% 0.62/0.82 ((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))) | icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))))),
% 0.62/0.82 inference(tautology,[status(thm)],[])).
% 0.62/0.82 tff(131,plain,
% 0.62/0.82 ((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[130, 129, 114])).
% 0.62/0.82 tff(132,plain,
% 0.62/0.82 (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[131, 77])).
% 0.62/0.82 tff(133,plain,
% 0.62/0.82 (((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))) | iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))),
% 0.62/0.82 inference(tautology,[status(thm)],[])).
% 0.62/0.82 tff(134,plain,
% 0.62/0.82 (iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.62/0.82 tff(135,plain,
% 0.62/0.82 (((~ic(BNODE_x1!143)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X)))) | ![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))),
% 0.62/0.82 inference(tautology,[status(thm)],[])).
% 0.62/0.82 tff(136,plain,
% 0.62/0.82 (![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[135, 112])).
% 0.62/0.82 tff(137,plain,
% 0.62/0.82 (((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))) | ((~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X1_116(uri_ex_p)))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X1_116(uri_ex_p)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(138,plain,
% 0.62/0.82 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))) | ((~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X1_116(uri_ex_p)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(139,plain,
% 0.62/0.82 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X1_116(uri_ex_p))),
% 0.62/0.82 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.62/0.82 tff(140,plain,
% 0.62/0.82 (icext(BNODE_x1!143, tptp_fun_X1_116(uri_ex_p))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[139, 136, 134])).
% 0.62/0.82 tff(141,plain,
% 0.62/0.82 ((~(icext(BNODE_x1!143, tptp_fun_X1_116(uri_ex_p)) <=> (tptp_fun_X1_116(uri_ex_p) = uri_ex_w))) | (~icext(BNODE_x1!143, tptp_fun_X1_116(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = uri_ex_w)),
% 0.62/0.82 inference(tautology,[status(thm)],[])).
% 0.62/0.82 tff(142,plain,
% 0.62/0.82 ((~(icext(BNODE_x1!143, tptp_fun_X1_116(uri_ex_p)) <=> (tptp_fun_X1_116(uri_ex_p) = uri_ex_w))) | (tptp_fun_X1_116(uri_ex_p) = uri_ex_w)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.62/0.82 tff(143,plain,
% 0.62/0.82 (tptp_fun_X1_116(uri_ex_p) = uri_ex_w),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[142, 46])).
% 0.62/0.82 tff(144,plain,
% 0.62/0.82 ((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) <=> (uri_ex_w = tptp_fun_X2_115(uri_ex_p))),
% 0.62/0.82 inference(monotonicity,[status(thm)],[143])).
% 0.62/0.82 tff(145,plain,
% 0.62/0.82 ((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_w)),
% 0.62/0.82 inference(transitivity,[status(thm)],[144, 1])).
% 0.62/0.82 tff(146,plain,
% 0.62/0.82 ((tptp_fun_X2_115(uri_ex_p) = uri_ex_w) <=> (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))),
% 0.62/0.82 inference(symmetry,[status(thm)],[145])).
% 0.62/0.82 tff(147,plain,
% 0.62/0.82 ((~![X: $i] : (icext(BNODE_x1!143, X) <=> (X = uri_ex_w))) | (icext(BNODE_x1!143, tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_w))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(148,plain,
% 0.62/0.82 (icext(BNODE_x1!143, tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_w)),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[147, 44])).
% 0.62/0.82 tff(149,plain,
% 0.62/0.82 (((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))) | iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))),
% 0.62/0.82 inference(tautology,[status(thm)],[])).
% 0.62/0.82 tff(150,plain,
% 0.62/0.82 (iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))),
% 0.62/0.82 inference(unit_resolution,[status(thm)],[149, 132])).
% 0.62/0.82 tff(151,plain,
% 0.62/0.82 (((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))) | ((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X2_115(uri_ex_p)))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X2_115(uri_ex_p)))),
% 0.62/0.82 inference(rewrite,[status(thm)],[])).
% 0.62/0.82 tff(152,plain,
% 0.62/0.82 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))) | ((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X2_115(uri_ex_p)))),
% 0.62/0.82 inference(quant_inst,[status(thm)],[])).
% 0.62/0.82 tff(153,plain,
% 0.62/0.82 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x1!143, X))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(BNODE_x1!143, tptp_fun_X2_115(uri_ex_p))),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.62/0.84 tff(154,plain,
% 0.62/0.84 (icext(BNODE_x1!143, tptp_fun_X2_115(uri_ex_p))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[153, 136, 150])).
% 0.62/0.84 tff(155,plain,
% 0.62/0.84 ((~(icext(BNODE_x1!143, tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_w))) | (~icext(BNODE_x1!143, tptp_fun_X2_115(uri_ex_p))) | (tptp_fun_X2_115(uri_ex_p) = uri_ex_w)),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(156,plain,
% 0.62/0.84 ((~(icext(BNODE_x1!143, tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_w))) | (tptp_fun_X2_115(uri_ex_p) = uri_ex_w)),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.62/0.84 tff(157,plain,
% 0.62/0.84 (tptp_fun_X2_115(uri_ex_p) = uri_ex_w),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[156, 148])).
% 0.62/0.84 tff(158,plain,
% 0.62/0.84 (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)),
% 0.62/0.84 inference(modus_ponens,[status(thm)],[157, 146])).
% 0.62/0.84 tff(159,plain,
% 0.62/0.84 (((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))) | (~(tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))),
% 0.62/0.84 inference(tautology,[status(thm)],[])).
% 0.62/0.84 tff(160,plain,
% 0.62/0.84 (~(tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[159, 132])).
% 0.62/0.84 tff(161,plain,
% 0.62/0.84 ($false),
% 0.62/0.84 inference(unit_resolution,[status(thm)],[160, 158])).
% 0.62/0.84 % SZS output end Proof
% 0.69/0.84 % E exiting
%------------------------------------------------------------------------------