%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB028+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:29:41 AM UTC 2025
% Result : Theorem 0.61s 0.82s
% Output : Proof 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWB028+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 07:54:12 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.61/0.82 % SZS status Theorem
% 0.61/0.82 % SZS output start Proof
% 0.61/0.82 tff(iext_type, type, (
% 0.61/0.82 iext: ( $i * $i * $i ) > $o)).
% 0.61/0.82 tff(tptp_fun_X2_115_type, type, (
% 0.61/0.82 tptp_fun_X2_115: $i > $i)).
% 0.61/0.82 tff(tptp_fun_X_61_type, type, (
% 0.61/0.82 tptp_fun_X_61: ( $i * $i ) > $i)).
% 0.61/0.82 tff(uri_ex_InversesOfFunctionalProperties_type, type, (
% 0.61/0.82 uri_ex_InversesOfFunctionalProperties: $i)).
% 0.61/0.82 tff(uri_owl_InverseFunctionalProperty_type, type, (
% 0.61/0.82 uri_owl_InverseFunctionalProperty: $i)).
% 0.61/0.82 tff(tptp_fun_Y_114_type, type, (
% 0.61/0.82 tptp_fun_Y_114: $i > $i)).
% 0.61/0.82 tff(tptp_fun_Y_42_type, type, (
% 0.61/0.82 tptp_fun_Y_42: ( $i * $i * $i ) > $i)).
% 0.61/0.82 tff(uri_owl_inverseOf_type, type, (
% 0.61/0.82 uri_owl_inverseOf: $i)).
% 0.61/0.82 tff(uri_owl_FunctionalProperty_type, type, (
% 0.61/0.82 uri_owl_FunctionalProperty: $i)).
% 0.61/0.82 tff(ip_type, type, (
% 0.61/0.82 ip: $i > $o)).
% 0.61/0.82 tff(tptp_fun_X_108_type, type, (
% 0.61/0.82 tptp_fun_X_108: ( $i * $i ) > $i)).
% 0.61/0.82 tff(tptp_fun_Y_107_type, type, (
% 0.61/0.82 tptp_fun_Y_107: ( $i * $i ) > $i)).
% 0.61/0.82 tff(icext_type, type, (
% 0.61/0.82 icext: ( $i * $i ) > $o)).
% 0.61/0.82 tff(tptp_fun_BNODE_z_140_type, type, (
% 0.61/0.82 tptp_fun_BNODE_z_140: $i)).
% 0.61/0.82 tff(uri_owl_someValuesFrom_type, type, (
% 0.61/0.82 uri_owl_someValuesFrom: $i)).
% 0.61/0.82 tff(uri_owl_onProperty_type, type, (
% 0.61/0.82 uri_owl_onProperty: $i)).
% 0.61/0.82 tff(uri_owl_Restriction_type, type, (
% 0.61/0.82 uri_owl_Restriction: $i)).
% 0.61/0.82 tff(uri_rdf_type_type, type, (
% 0.61/0.82 uri_rdf_type: $i)).
% 0.61/0.82 tff(uri_owl_equivalentClass_type, type, (
% 0.61/0.82 uri_owl_equivalentClass: $i)).
% 0.61/0.82 tff(ic_type, type, (
% 0.61/0.82 ic: $i > $o)).
% 0.61/0.82 tff(tptp_fun_X_67_type, type, (
% 0.61/0.82 tptp_fun_X_67: ( $i * $i ) > $i)).
% 0.61/0.82 tff(uri_rdfs_subClassOf_type, type, (
% 0.61/0.82 uri_rdfs_subClassOf: $i)).
% 0.61/0.82 tff(tptp_fun_X1_116_type, type, (
% 0.61/0.82 tptp_fun_X1_116: $i > $i)).
% 0.61/0.82 tff(tptp_fun_Y2_111_type, type, (
% 0.61/0.82 tptp_fun_Y2_111: $i > $i)).
% 0.61/0.82 tff(tptp_fun_Y1_112_type, type, (
% 0.61/0.82 tptp_fun_Y1_112: $i > $i)).
% 0.61/0.82 tff(tptp_fun_X_113_type, type, (
% 0.61/0.82 tptp_fun_X_113: $i > $i)).
% 0.61/0.82 tff(1,plain,
% 0.61/0.82 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))))))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(2,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.61/0.82 inference(quant_intro,[status(thm)],[1])).
% 0.61/0.82 tff(3,plain,
% 0.61/0.82 (^[P1: $i, P2: $i] : refl((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(4,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.61/0.82 inference(quant_intro,[status(thm)],[3])).
% 0.61/0.82 tff(5,plain,
% 0.61/0.82 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(6,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.61/0.82 inference(quant_intro,[status(thm)],[5])).
% 0.61/0.82 tff(7,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.61/0.82 inference(transitivity,[status(thm)],[6, 4])).
% 0.61/0.82 tff(8,plain,
% 0.61/0.82 (^[P1: $i, P2: $i] : trans(monotonicity(rewrite(((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))), trans(monotonicity(rewrite((~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))) <=> (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))), ((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))), rewrite((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))), ((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))), ((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) <=> (((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))), rewrite((((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))), ((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(9,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.61/0.82 inference(quant_intro,[status(thm)],[8])).
% 0.61/0.82 tff(10,plain,
% 0.61/0.82 (^[P1: $i, P2: $i] : rewrite((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(11,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> ![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))),
% 0.61/0.82 inference(quant_intro,[status(thm)],[10])).
% 0.61/0.82 tff(12,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.61/0.82 inference(rewrite,[status(thm)],[])).
% 0.61/0.82 tff(13,plain,
% 0.61/0.82 (^[P1: $i, P2: $i] : rewrite((iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))),
% 0.61/0.82 inference(bind,[status(th)],[])).
% 0.61/0.82 tff(14,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.61/0.82 inference(quant_intro,[status(thm)],[13])).
% 0.61/0.82 tff(15,axiom,(![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_inv')).
% 0.61/0.82 tff(16,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.61/0.82 tff(17,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.61/0.82 tff(18,plain,(
% 0.61/0.82 ![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))),
% 0.61/0.82 inference(skolemize,[status(sab)],[17])).
% 0.61/0.82 tff(19,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.61/0.82 tff(20,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.61/0.82 tff(21,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.61/0.82 tff(22,plain,
% 0.61/0.82 (![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.61/0.82 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.61/0.82 tff(23,plain,
% 0.61/0.82 (((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X)))))))))) <=> ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X))))))))))),
% 0.61/0.82 inference(rewrite,[status(thm)],[])).
% 0.61/0.82 tff(24,plain,
% 0.61/0.82 ((~((~(iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X))))))))) <=> (~((~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X)))))))))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(25,plain,
% 0.61/0.83 (((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X)))))))))) <=> ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X))))))))))),
% 0.61/0.83 inference(monotonicity,[status(thm)],[24])).
% 0.61/0.83 tff(26,plain,
% 0.61/0.83 (((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X)))))))))) <=> ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X))))))))))),
% 0.61/0.83 inference(transitivity,[status(thm)],[25, 23])).
% 0.61/0.83 tff(27,plain,
% 0.61/0.83 ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X)))))))))),
% 0.61/0.83 inference(quant_inst,[status(thm)],[])).
% 0.61/0.83 tff(28,plain,
% 0.61/0.83 ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X)))))))))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.61/0.83 tff(29,plain,
% 0.61/0.83 (~((~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X))))))))),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.61/0.83 tff(30,plain,
% 0.61/0.83 (((~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_107(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X_108(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X)))))))) | ((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X))))))),
% 0.61/0.83 inference(tautology,[status(thm)],[])).
% 0.61/0.83 tff(31,plain,
% 0.61/0.83 ((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X)))))),
% 0.61/0.83 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.61/0.83 tff(32,plain,
% 0.61/0.83 (?[BNODE_z: $i] : (iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf) & iext(uri_owl_someValuesFrom, BNODE_z, uri_owl_FunctionalProperty)) <=> ?[BNODE_z: $i] : (iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf) & iext(uri_owl_someValuesFrom, BNODE_z, uri_owl_FunctionalProperty))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(33,plain,
% 0.61/0.83 (^[BNODE_z: $i] : trans(monotonicity(rewrite(((iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf)) <=> (iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf))), ((((iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf)) & iext(uri_owl_someValuesFrom, BNODE_z, uri_owl_FunctionalProperty)) <=> ((iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf)) & iext(uri_owl_someValuesFrom, BNODE_z, uri_owl_FunctionalProperty)))), rewrite(((iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf)) & iext(uri_owl_someValuesFrom, BNODE_z, uri_owl_FunctionalProperty)) <=> (iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf) & iext(uri_owl_someValuesFrom, BNODE_z, uri_owl_FunctionalProperty))), ((((iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf)) & iext(uri_owl_someValuesFrom, BNODE_z, uri_owl_FunctionalProperty)) <=> (iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf) & iext(uri_owl_someValuesFrom, BNODE_z, uri_owl_FunctionalProperty))))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(34,plain,
% 0.61/0.83 (?[BNODE_z: $i] : (((iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf)) & iext(uri_owl_someValuesFrom, BNODE_z, uri_owl_FunctionalProperty)) <=> ?[BNODE_z: $i] : (iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf) & iext(uri_owl_someValuesFrom, BNODE_z, uri_owl_FunctionalProperty))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[33])).
% 0.61/0.83 tff(35,axiom,(?[BNODE_z: $i] : (((iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction)) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf)) & iext(uri_owl_someValuesFrom, BNODE_z, uri_owl_FunctionalProperty))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_premise_fullish_028_Inferred_Property_Characteristics_III')).
% 0.61/0.83 tff(36,plain,
% 0.61/0.83 (?[BNODE_z: $i] : (iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf) & iext(uri_owl_someValuesFrom, BNODE_z, uri_owl_FunctionalProperty))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.61/0.83 tff(37,plain,
% 0.61/0.83 (?[BNODE_z: $i] : (iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z) & iext(uri_rdf_type, BNODE_z, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z, uri_owl_inverseOf) & iext(uri_owl_someValuesFrom, BNODE_z, uri_owl_FunctionalProperty))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.61/0.83 tff(38,plain,(
% 0.61/0.83 iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140) & iext(uri_rdf_type, BNODE_z!140, uri_owl_Restriction) & iext(uri_owl_onProperty, BNODE_z!140, uri_owl_inverseOf) & iext(uri_owl_someValuesFrom, BNODE_z!140, uri_owl_FunctionalProperty)),
% 0.61/0.83 inference(skolemize,[status(sab)],[37])).
% 0.61/0.83 tff(39,plain,
% 0.61/0.83 (iext(uri_owl_someValuesFrom, BNODE_z!140, uri_owl_FunctionalProperty)),
% 0.61/0.83 inference(and_elim,[status(thm)],[38])).
% 0.61/0.83 tff(40,plain,
% 0.61/0.83 (iext(uri_owl_onProperty, BNODE_z!140, uri_owl_inverseOf)),
% 0.61/0.83 inference(and_elim,[status(thm)],[38])).
% 0.61/0.83 tff(41,plain,
% 0.61/0.83 (^[Z: $i, P: $i, C: $i] : rewrite(((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(42,plain,
% 0.61/0.83 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[41])).
% 0.61/0.83 tff(43,plain,
% 0.61/0.83 (^[Z: $i, P: $i, C: $i] : refl(((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(44,plain,
% 0.61/0.83 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[43])).
% 0.61/0.83 tff(45,plain,
% 0.61/0.83 (^[Z: $i, P: $i, C: $i] : rewrite(((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(46,plain,
% 0.61/0.83 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[45])).
% 0.61/0.83 tff(47,plain,
% 0.61/0.83 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 0.61/0.83 inference(transitivity,[status(thm)],[46, 44])).
% 0.61/0.83 tff(48,plain,
% 0.61/0.83 (^[Z: $i, P: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) <=> (~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))))), ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) <=> (~(~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))))))), rewrite((~(~((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)))), ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) <=> ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))))), quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite(((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) <=> ((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))), rewrite((icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))) <=> (icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))), ((((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))) <=> (((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P)))))) & (icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))), rewrite((((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P)))))) & (icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))) <=> (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))), ((((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))) <=> (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))))), (![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))) <=> ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))), (((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))))) <=> (((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))))), rewrite((((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C))) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y)))))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))), (((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))))) <=> ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(49,plain,
% 0.61/0.83 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y)))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[48])).
% 0.61/0.83 tff(50,plain,
% 0.61/0.83 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 0.61/0.83 inference(rewrite,[status(thm)],[])).
% 0.61/0.83 tff(51,plain,
% 0.61/0.83 (^[Z: $i, P: $i, C: $i] : rewrite(((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))))),
% 0.61/0.83 inference(bind,[status(th)],[])).
% 0.61/0.83 tff(52,plain,
% 0.61/0.83 (![Z: $i, P: $i, C: $i] : ((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 0.61/0.83 inference(quant_intro,[status(thm)],[51])).
% 0.61/0.83 tff(53,axiom,(![Z: $i, P: $i, C: $i] : ((iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_restrict_somevaluesfrom')).
% 0.61/0.83 tff(54,plain,
% 0.61/0.83 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.61/0.83 tff(55,plain,
% 0.61/0.83 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ?[Y: $i] : (iext(P, X, Y) & icext(C, Y))))),
% 0.61/0.83 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.61/0.83 tff(56,plain,(
% 0.61/0.83 ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_someValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | (iext(P, X, tptp_fun_Y_42(X, C, P)) & icext(C, tptp_fun_Y_42(X, C, P)))) & (icext(Z, X) | ![Y: $i] : (~(iext(P, X, Y) & icext(C, Y))))))),
% 0.61/0.84 inference(skolemize,[status(sab)],[55])).
% 0.61/0.84 tff(57,plain,
% 0.61/0.84 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.61/0.84 tff(58,plain,
% 0.61/0.84 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))) | (~iext(uri_owl_someValuesFrom, Z, C)))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.61/0.84 tff(59,plain,
% 0.61/0.84 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[58, 42])).
% 0.61/0.84 tff(60,plain,
% 0.61/0.84 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, BNODE_z!140, uri_owl_inverseOf)) | (~iext(uri_owl_someValuesFrom, BNODE_z!140, uri_owl_FunctionalProperty)) | ![X: $i] : (~((~(icext(BNODE_z!140, X) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, X, Y))))) | (~((~icext(BNODE_z!140, X)) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, X, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | (~iext(uri_owl_onProperty, BNODE_z!140, uri_owl_inverseOf)) | (~iext(uri_owl_someValuesFrom, BNODE_z!140, uri_owl_FunctionalProperty)) | ![X: $i] : (~((~(icext(BNODE_z!140, X) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, X, Y))))) | (~((~icext(BNODE_z!140, X)) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, X, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))))))))))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.84 tff(61,plain,
% 0.61/0.84 (((~iext(uri_owl_onProperty, BNODE_z!140, uri_owl_inverseOf)) | (~iext(uri_owl_someValuesFrom, BNODE_z!140, uri_owl_FunctionalProperty)) | ![X: $i] : (~((~((~icext(BNODE_z!140, X)) | (~((~iext(uri_owl_inverseOf, X, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~(icext(BNODE_z!140, X) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, X, Y)))))))) <=> ((~iext(uri_owl_onProperty, BNODE_z!140, uri_owl_inverseOf)) | (~iext(uri_owl_someValuesFrom, BNODE_z!140, uri_owl_FunctionalProperty)) | ![X: $i] : (~((~(icext(BNODE_z!140, X) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, X, Y))))) | (~((~icext(BNODE_z!140, X)) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, X, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))))))))))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.84 tff(62,plain,
% 0.61/0.84 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, BNODE_z!140, uri_owl_inverseOf)) | (~iext(uri_owl_someValuesFrom, BNODE_z!140, uri_owl_FunctionalProperty)) | ![X: $i] : (~((~((~icext(BNODE_z!140, X)) | (~((~iext(uri_owl_inverseOf, X, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~(icext(BNODE_z!140, X) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, X, Y))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, BNODE_z!140, uri_owl_inverseOf)) | (~iext(uri_owl_someValuesFrom, BNODE_z!140, uri_owl_FunctionalProperty)) | ![X: $i] : (~((~(icext(BNODE_z!140, X) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, X, Y))))) | (~((~icext(BNODE_z!140, X)) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, X, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf)))))))))))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[61])).
% 0.61/0.84 tff(63,plain,
% 0.61/0.84 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, BNODE_z!140, uri_owl_inverseOf)) | (~iext(uri_owl_someValuesFrom, BNODE_z!140, uri_owl_FunctionalProperty)) | ![X: $i] : (~((~((~icext(BNODE_z!140, X)) | (~((~iext(uri_owl_inverseOf, X, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~(icext(BNODE_z!140, X) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, X, Y))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | (~iext(uri_owl_onProperty, BNODE_z!140, uri_owl_inverseOf)) | (~iext(uri_owl_someValuesFrom, BNODE_z!140, uri_owl_FunctionalProperty)) | ![X: $i] : (~((~(icext(BNODE_z!140, X) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, X, Y))))) | (~((~icext(BNODE_z!140, X)) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, X, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))))))))))),
% 0.61/0.84 inference(transitivity,[status(thm)],[62, 60])).
% 0.61/0.84 tff(64,plain,
% 0.61/0.84 ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | ((~iext(uri_owl_onProperty, BNODE_z!140, uri_owl_inverseOf)) | (~iext(uri_owl_someValuesFrom, BNODE_z!140, uri_owl_FunctionalProperty)) | ![X: $i] : (~((~((~icext(BNODE_z!140, X)) | (~((~iext(uri_owl_inverseOf, X, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~(icext(BNODE_z!140, X) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, X, Y))))))))),
% 0.61/0.84 inference(quant_inst,[status(thm)],[])).
% 0.61/0.84 tff(65,plain,
% 0.61/0.84 ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_onProperty, Z, P)) | (~iext(uri_owl_someValuesFrom, Z, C)) | ![X: $i] : (~((~((~icext(Z, X)) | (~((~iext(P, X, tptp_fun_Y_42(X, C, P))) | (~icext(C, tptp_fun_Y_42(X, C, P))))))) | (~(icext(Z, X) | ![Y: $i] : ((~icext(C, Y)) | (~iext(P, X, Y))))))))) | (~iext(uri_owl_onProperty, BNODE_z!140, uri_owl_inverseOf)) | (~iext(uri_owl_someValuesFrom, BNODE_z!140, uri_owl_FunctionalProperty)) | ![X: $i] : (~((~(icext(BNODE_z!140, X) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, X, Y))))) | (~((~icext(BNODE_z!140, X)) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, X, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf)))))))))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.61/0.84 tff(66,plain,
% 0.61/0.84 (![X: $i] : (~((~(icext(BNODE_z!140, X) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, X, Y))))) | (~((~icext(BNODE_z!140, X)) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, X, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf)))))))))),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[65, 59, 40, 39])).
% 0.61/0.84 tff(67,plain,
% 0.61/0.84 ((~![X: $i] : (~((~(icext(BNODE_z!140, X) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, X, Y))))) | (~((~icext(BNODE_z!140, X)) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, X, tptp_fun_Y_42(X, uri_owl_FunctionalProperty, uri_owl_inverseOf)))))))))) | (~((~(icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), Y))))) | (~((~icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))))))))),
% 0.61/0.84 inference(quant_inst,[status(thm)],[])).
% 0.61/0.84 tff(68,plain,
% 0.61/0.84 (~((~(icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), Y))))) | (~((~icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))))),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.61/0.84 tff(69,plain,
% 0.61/0.84 (((~(icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | ![Y: $i] : ((~icext(uri_owl_FunctionalProperty, Y)) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), Y))))) | (~((~icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))))))) | ((~icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))),
% 0.61/0.84 inference(tautology,[status(thm)],[])).
% 0.61/0.84 tff(70,plain,
% 0.61/0.84 ((~icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))))),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.61/0.84 tff(71,plain,
% 0.61/0.84 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))))))),
% 0.61/0.84 inference(bind,[status(th)],[])).
% 0.61/0.84 tff(72,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 0.61/0.84 inference(quant_intro,[status(thm)],[71])).
% 0.61/0.84 tff(73,plain,
% 0.61/0.84 (^[C1: $i, C2: $i] : refl((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))))),
% 0.61/0.84 inference(bind,[status(th)],[])).
% 0.61/0.84 tff(74,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 0.61/0.84 inference(quant_intro,[status(thm)],[73])).
% 0.61/0.84 tff(75,plain,
% 0.61/0.84 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))))),
% 0.61/0.84 inference(bind,[status(th)],[])).
% 0.61/0.84 tff(76,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 0.61/0.84 inference(quant_intro,[status(thm)],[75])).
% 0.61/0.84 tff(77,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 0.61/0.84 inference(transitivity,[status(thm)],[76, 74])).
% 0.61/0.84 tff(78,plain,
% 0.61/0.84 (^[C1: $i, C2: $i] : trans(monotonicity(rewrite(((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))), trans(monotonicity(rewrite((~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))) <=> (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))), rewrite((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))), ((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) <=> (((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))), rewrite((((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))), ((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))))),
% 0.61/0.84 inference(bind,[status(th)],[])).
% 0.61/0.84 tff(79,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 0.61/0.84 inference(quant_intro,[status(thm)],[78])).
% 0.61/0.84 tff(80,plain,
% 0.61/0.84 (^[C1: $i, C2: $i] : rewrite((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 0.61/0.84 inference(bind,[status(th)],[])).
% 0.61/0.84 tff(81,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> ![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))),
% 0.61/0.84 inference(quant_intro,[status(thm)],[80])).
% 0.61/0.84 tff(82,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.84 tff(83,plain,
% 0.61/0.84 (^[C1: $i, C2: $i] : rewrite((iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))))),
% 0.61/0.84 inference(bind,[status(th)],[])).
% 0.61/0.84 tff(84,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.61/0.84 inference(quant_intro,[status(thm)],[83])).
% 0.61/0.84 tff(85,axiom,(![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_eqdis_equivalentclass')).
% 0.61/0.84 tff(86,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.61/0.84 tff(87,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.61/0.84 tff(88,plain,(
% 0.61/0.84 ![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 0.61/0.84 inference(skolemize,[status(sab)],[87])).
% 0.61/0.84 tff(89,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.61/0.84 tff(90,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.61/0.84 tff(91,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[90, 77])).
% 0.61/0.84 tff(92,plain,
% 0.61/0.84 (![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[91, 72])).
% 0.61/0.84 tff(93,plain,
% 0.61/0.84 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(BNODE_z!140)) | (~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(BNODE_z!140)) | (~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X))))))))))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.84 tff(94,plain,
% 0.61/0.84 ((~((~(iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140) | (~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X))))))))) <=> (~((~(iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(BNODE_z!140)) | (~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X)))))))))),
% 0.61/0.84 inference(rewrite,[status(thm)],[])).
% 0.61/0.84 tff(95,plain,
% 0.61/0.84 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140) | (~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(BNODE_z!140)) | (~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X))))))))))),
% 0.61/0.84 inference(monotonicity,[status(thm)],[94])).
% 0.61/0.84 tff(96,plain,
% 0.61/0.84 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140) | (~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(BNODE_z!140)) | (~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X))))))))))),
% 0.61/0.84 inference(transitivity,[status(thm)],[95, 93])).
% 0.61/0.84 tff(97,plain,
% 0.61/0.84 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140) | (~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X)))))))))),
% 0.61/0.84 inference(quant_inst,[status(thm)],[])).
% 0.61/0.84 tff(98,plain,
% 0.61/0.84 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(BNODE_z!140)) | (~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X)))))))))),
% 0.61/0.84 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.61/0.84 tff(99,plain,
% 0.61/0.84 (~((~(iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(BNODE_z!140)) | (~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X))))))))),
% 0.61/0.84 inference(unit_resolution,[status(thm)],[98, 92])).
% 0.61/0.84 tff(100,plain,
% 0.61/0.84 (((~(iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(BNODE_z!140)) | (~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_67(BNODE_z!140, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X)))))))) | ((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X))))))),
% 0.69/0.84 inference(tautology,[status(thm)],[])).
% 0.69/0.84 tff(101,plain,
% 0.69/0.84 ((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X)))))),
% 0.69/0.84 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.69/0.84 tff(102,plain,
% 0.69/0.84 (iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)),
% 0.69/0.84 inference(and_elim,[status(thm)],[38])).
% 0.69/0.84 tff(103,plain,
% 0.69/0.84 ((~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X))))))) | (~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X)))))),
% 0.69/0.84 inference(tautology,[status(thm)],[])).
% 0.69/0.84 tff(104,plain,
% 0.69/0.84 ((~((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X))))))) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X)))))),
% 0.69/0.84 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.69/0.84 tff(105,plain,
% 0.69/0.84 (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X))))),
% 0.69/0.84 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.69/0.84 tff(106,plain,
% 0.69/0.84 (((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X)))) | ![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X))),
% 0.69/0.84 inference(tautology,[status(thm)],[])).
% 0.69/0.84 tff(107,plain,
% 0.69/0.84 (![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X))),
% 0.69/0.84 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.69/0.84 tff(108,plain,
% 0.69/0.84 ((~![X: $i] : (icext(uri_ex_InversesOfFunctionalProperties, X) <=> icext(BNODE_z!140, X))) | (icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.84 inference(quant_inst,[status(thm)],[])).
% 0.69/0.84 tff(109,plain,
% 0.69/0.84 (icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))),
% 0.69/0.84 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.69/0.84 tff(110,plain,
% 0.69/0.84 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))))))),
% 0.69/0.84 inference(bind,[status(th)],[])).
% 0.69/0.84 tff(111,plain,
% 0.69/0.84 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))),
% 0.69/0.84 inference(quant_intro,[status(thm)],[110])).
% 0.69/0.84 tff(112,plain,
% 0.69/0.84 (^[C1: $i, C2: $i] : refl((~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))))),
% 0.69/0.84 inference(bind,[status(th)],[])).
% 0.69/0.84 tff(113,plain,
% 0.69/0.84 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.69/0.84 inference(quant_intro,[status(thm)],[112])).
% 0.69/0.84 tff(114,plain,
% 0.69/0.84 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))))),
% 0.69/0.84 inference(bind,[status(th)],[])).
% 0.69/0.84 tff(115,plain,
% 0.69/0.84 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.69/0.84 inference(quant_intro,[status(thm)],[114])).
% 0.69/0.84 tff(116,plain,
% 0.69/0.84 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.69/0.84 inference(transitivity,[status(thm)],[115, 113])).
% 0.69/0.85 tff(117,plain,
% 0.69/0.85 (^[C1: $i, C2: $i] : trans(monotonicity(rewrite(((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) <=> ((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))), rewrite((iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))) <=> (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))), ((((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) <=> (((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))), rewrite((((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) <=> (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))), ((((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) <=> (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(118,plain,
% 0.69/0.85 (![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[117])).
% 0.69/0.85 tff(119,plain,
% 0.69/0.85 (^[C1: $i, C2: $i] : rewrite((((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))) <=> (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(120,plain,
% 0.69/0.85 (![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))) <=> ![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[119])).
% 0.69/0.85 tff(121,plain,
% 0.69/0.85 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(122,plain,
% 0.69/0.85 (^[C1: $i, C2: $i] : rewrite((iext(uri_rdfs_subClassOf, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) => icext(C2, X)))) <=> (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(123,plain,
% 0.69/0.85 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) => icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[122])).
% 0.69/0.85 tff(124,axiom,(![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) => icext(C2, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_rdfsext_subclassof')).
% 0.69/0.85 tff(125,plain,
% 0.69/0.85 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.69/0.85 tff(126,plain,
% 0.69/0.85 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.69/0.85 tff(127,plain,(
% 0.69/0.85 ![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))),
% 0.69/0.85 inference(skolemize,[status(sab)],[126])).
% 0.69/0.85 tff(128,plain,
% 0.69/0.85 (![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.69/0.85 tff(129,plain,
% 0.69/0.85 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[128, 118])).
% 0.69/0.85 tff(130,plain,
% 0.69/0.85 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[129, 116])).
% 0.69/0.85 tff(131,plain,
% 0.69/0.85 (![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[130, 111])).
% 0.69/0.85 tff(132,plain,
% 0.69/0.85 (((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)) | (~((~![X: $i] : ((~icext(uri_ex_InversesOfFunctionalProperties, X)) | icext(uri_owl_InverseFunctionalProperty, X))) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)) | (~((~![X: $i] : ((~icext(uri_ex_InversesOfFunctionalProperties, X)) | icext(uri_owl_InverseFunctionalProperty, X))) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)))))))))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(133,plain,
% 0.69/0.85 ((~((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_owl_InverseFunctionalProperty)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)) | (~((~ic(uri_owl_InverseFunctionalProperty)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : ((~icext(uri_ex_InversesOfFunctionalProperties, X)) | icext(uri_owl_InverseFunctionalProperty, X))))))))) <=> (~((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)) | (~((~![X: $i] : ((~icext(uri_ex_InversesOfFunctionalProperties, X)) | icext(uri_owl_InverseFunctionalProperty, X))) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty))))))))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(134,plain,
% 0.69/0.85 (((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_owl_InverseFunctionalProperty)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)) | (~((~ic(uri_owl_InverseFunctionalProperty)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : ((~icext(uri_ex_InversesOfFunctionalProperties, X)) | icext(uri_owl_InverseFunctionalProperty, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)) | (~((~![X: $i] : ((~icext(uri_ex_InversesOfFunctionalProperties, X)) | icext(uri_owl_InverseFunctionalProperty, X))) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)))))))))),
% 0.69/0.85 inference(monotonicity,[status(thm)],[133])).
% 0.69/0.85 tff(135,plain,
% 0.69/0.85 (((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_owl_InverseFunctionalProperty)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)) | (~((~ic(uri_owl_InverseFunctionalProperty)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : ((~icext(uri_ex_InversesOfFunctionalProperties, X)) | icext(uri_owl_InverseFunctionalProperty, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)) | (~((~![X: $i] : ((~icext(uri_ex_InversesOfFunctionalProperties, X)) | icext(uri_owl_InverseFunctionalProperty, X))) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)))))))))),
% 0.69/0.85 inference(transitivity,[status(thm)],[134, 132])).
% 0.69/0.85 tff(136,plain,
% 0.69/0.85 ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_owl_InverseFunctionalProperty)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)) | (~((~ic(uri_owl_InverseFunctionalProperty)) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~![X: $i] : ((~icext(uri_ex_InversesOfFunctionalProperties, X)) | icext(uri_owl_InverseFunctionalProperty, X)))))))))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(137,plain,
% 0.69/0.85 ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)) | (~((~![X: $i] : ((~icext(uri_ex_InversesOfFunctionalProperties, X)) | icext(uri_owl_InverseFunctionalProperty, X))) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty))))))))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.69/0.85 tff(138,plain,
% 0.69/0.85 (~((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)) | (~((~![X: $i] : ((~icext(uri_ex_InversesOfFunctionalProperties, X)) | icext(uri_owl_InverseFunctionalProperty, X))) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)))))))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[137, 131])).
% 0.69/0.85 tff(139,plain,
% 0.69/0.85 (((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)) | (~((~![X: $i] : ((~icext(uri_ex_InversesOfFunctionalProperties, X)) | icext(uri_owl_InverseFunctionalProperty, X))) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty))))))) | (iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))),
% 0.69/0.85 inference(tautology,[status(thm)],[])).
% 0.69/0.85 tff(140,plain,
% 0.69/0.85 (iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.69/0.85 tff(141,plain,
% 0.69/0.85 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X))))) <=> ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X))))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(142,plain,
% 0.69/0.85 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[141])).
% 0.69/0.85 tff(143,plain,
% 0.69/0.85 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y))) <=> ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X))))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(144,plain,
% 0.69/0.85 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[143])).
% 0.69/0.85 tff(145,plain,
% 0.69/0.85 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(146,plain,
% 0.69/0.85 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_equivalentClass, X, Y) => (ic(X) & ic(Y))) <=> ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(147,plain,
% 0.69/0.85 (![X: $i, Y: $i] : (iext(uri_owl_equivalentClass, X, Y) => (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[146])).
% 0.69/0.85 tff(148,axiom,(![X: $i, Y: $i] : (iext(uri_owl_equivalentClass, X, Y) => (ic(X) & ic(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_prop_equivalentclass_ext')).
% 0.69/0.85 tff(149,plain,
% 0.69/0.85 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.69/0.85 tff(150,plain,
% 0.69/0.85 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.69/0.85 tff(151,plain,(
% 0.69/0.85 ![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y)))),
% 0.69/0.85 inference(skolemize,[status(sab)],[150])).
% 0.69/0.85 tff(152,plain,
% 0.69/0.85 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.69/0.85 tff(153,plain,
% 0.69/0.85 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[152, 142])).
% 0.69/0.85 tff(154,plain,
% 0.69/0.85 (((~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)))))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(155,plain,
% 0.69/0.85 ((~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)))))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(156,plain,
% 0.69/0.85 ((~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties, BNODE_z!140)) | (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties))))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.69/0.85 tff(157,plain,
% 0.69/0.85 (~((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[156, 153, 102])).
% 0.69/0.85 tff(158,plain,
% 0.69/0.85 (((~ic(BNODE_z!140)) | (~ic(uri_ex_InversesOfFunctionalProperties))) | ic(uri_ex_InversesOfFunctionalProperties)),
% 0.69/0.85 inference(tautology,[status(thm)],[])).
% 0.69/0.85 tff(159,plain,
% 0.69/0.85 (ic(uri_ex_InversesOfFunctionalProperties)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.69/0.85 tff(160,plain,
% 0.69/0.85 ((~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)) <=> (~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(161,axiom,(~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_028_Inferred_Property_Characteristics_III')).
% 0.69/0.85 tff(162,plain,
% 0.69/0.85 (~iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.69/0.85 tff(163,plain,
% 0.69/0.85 (ic(uri_owl_InverseFunctionalProperty) <=> ic(uri_owl_InverseFunctionalProperty)),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(164,axiom,(ic(uri_owl_InverseFunctionalProperty)), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_class_inversefunctionalproperty_type')).
% 0.69/0.85 tff(165,plain,
% 0.69/0.85 (ic(uri_owl_InverseFunctionalProperty)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.69/0.85 tff(166,plain,
% 0.69/0.85 ((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))),
% 0.69/0.85 inference(tautology,[status(thm)],[])).
% 0.69/0.85 tff(167,plain,
% 0.69/0.85 ((~(iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties, uri_owl_InverseFunctionalProperty) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~ic(uri_owl_InverseFunctionalProperty)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) | (~ic(uri_ex_InversesOfFunctionalProperties)) | (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[166, 165, 162])).
% 0.69/0.85 tff(168,plain,
% 0.69/0.85 (~((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[167, 159, 140])).
% 0.69/0.85 tff(169,plain,
% 0.69/0.85 (((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))),
% 0.69/0.85 inference(tautology,[status(thm)],[])).
% 0.69/0.85 tff(170,plain,
% 0.69/0.85 (icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.69/0.85 tff(171,plain,
% 0.69/0.85 ((~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))),
% 0.69/0.85 inference(tautology,[status(thm)],[])).
% 0.69/0.85 tff(172,plain,
% 0.69/0.85 ((~(icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) <=> icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.69/0.85 tff(173,plain,
% 0.69/0.85 (icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[172, 109])).
% 0.69/0.85 tff(174,plain,
% 0.69/0.85 ((~((~icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))))),
% 0.69/0.85 inference(tautology,[status(thm)],[])).
% 0.69/0.85 tff(175,plain,
% 0.69/0.85 ((~((~icext(BNODE_z!140, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.69/0.85 tff(176,plain,
% 0.69/0.85 (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[175, 70])).
% 0.69/0.85 tff(177,plain,
% 0.69/0.85 (((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))),
% 0.69/0.85 inference(tautology,[status(thm)],[])).
% 0.69/0.85 tff(178,plain,
% 0.69/0.85 (iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.69/0.85 tff(179,plain,
% 0.69/0.85 ((~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X))))))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X)))))),
% 0.69/0.85 inference(tautology,[status(thm)],[])).
% 0.69/0.85 tff(180,plain,
% 0.69/0.85 ((~((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X))))))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X)))))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.69/0.85 tff(181,plain,
% 0.69/0.85 (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X))))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[180, 31])).
% 0.69/0.85 tff(182,plain,
% 0.69/0.85 (((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X)))) | ![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X))),
% 0.69/0.85 inference(tautology,[status(thm)],[])).
% 0.69/0.85 tff(183,plain,
% 0.69/0.85 (![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.69/0.85 tff(184,plain,
% 0.69/0.85 ((~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X))) | (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))),
% 0.69/0.85 inference(quant_inst,[status(thm)],[])).
% 0.69/0.85 tff(185,plain,
% 0.69/0.85 (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.69/0.85 tff(186,plain,
% 0.69/0.85 (^[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)))))))))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(187,plain,
% 0.69/0.85 (![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))))))))))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[186])).
% 0.69/0.85 tff(188,plain,
% 0.69/0.85 (^[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))))))))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(189,plain,
% 0.69/0.85 (![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)))))))))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[188])).
% 0.69/0.85 tff(190,plain,
% 0.69/0.85 (^[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))))))))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(191,plain,
% 0.69/0.85 (![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)))))))))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[190])).
% 0.69/0.85 tff(192,plain,
% 0.69/0.85 (![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)))))))))),
% 0.69/0.85 inference(transitivity,[status(thm)],[191, 189])).
% 0.69/0.85 tff(193,plain,
% 0.69/0.85 (^[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)))))))))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(194,plain,
% 0.69/0.86 (![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)))))))))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[193])).
% 0.69/0.86 tff(195,plain,
% 0.69/0.86 (^[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)))))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(196,plain,
% 0.69/0.86 (![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))))))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[195])).
% 0.69/0.86 tff(197,plain,
% 0.69/0.86 (![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))))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(198,plain,
% 0.69/0.86 (^[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)))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(199,plain,
% 0.69/0.86 (![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))))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[198])).
% 0.69/0.86 tff(200,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/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_char_inversefunctional')).
% 0.69/0.86 tff(201,plain,
% 0.69/0.86 (![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))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.69/0.86 tff(202,plain,
% 0.69/0.86 (![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))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[201, 197])).
% 0.69/0.86 tff(203,plain,(
% 0.69/0.86 ![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)))))))),
% 0.69/0.86 inference(skolemize,[status(sab)],[202])).
% 0.69/0.86 tff(204,plain,
% 0.69/0.86 (![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))))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[203, 196])).
% 0.69/0.86 tff(205,plain,
% 0.69/0.86 (![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)))))))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[204, 194])).
% 0.69/0.86 tff(206,plain,
% 0.69/0.86 (![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)))))))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[205, 192])).
% 0.69/0.86 tff(207,plain,
% 0.69/0.86 (![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))))))))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[206, 187])).
% 0.69/0.86 tff(208,plain,
% 0.69/0.86 (((~![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, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X2, Y)) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), 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, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X2, Y)) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X1, Y)))))))))))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(209,plain,
% 0.69/0.86 ((~((~(icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X2, Y)) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X1, Y)))))))))) <=> (~((~(icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X2, Y)) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X1, Y))))))))))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(210,plain,
% 0.69/0.86 (((~![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, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X2, Y)) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), 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, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X2, Y)) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X1, Y)))))))))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[209])).
% 0.69/0.86 tff(211,plain,
% 0.69/0.86 (((~![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, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X2, Y)) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), 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, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X2, Y)) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X1, Y)))))))))))),
% 0.69/0.86 inference(transitivity,[status(thm)],[210, 208])).
% 0.69/0.86 tff(212,plain,
% 0.69/0.86 ((~![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, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X2, Y)) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X1, Y))))))))))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(213,plain,
% 0.69/0.86 ((~![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, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X2, Y)) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X1, Y))))))))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.69/0.86 tff(214,plain,
% 0.69/0.86 (~((~(icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X2, Y)) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X1, Y)))))))))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[213, 207])).
% 0.69/0.86 tff(215,plain,
% 0.69/0.86 (((~(icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X2, Y)) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X1, Y))))))))) | (icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))),
% 0.69/0.86 inference(tautology,[status(thm)],[])).
% 0.69/0.86 tff(216,plain,
% 0.69/0.86 (icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.69/0.86 tff(217,plain,
% 0.69/0.86 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X))))) <=> ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X))))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(218,plain,
% 0.69/0.86 (![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X)))))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[217])).
% 0.69/0.86 tff(219,plain,
% 0.69/0.86 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_inverseOf, X, Y)) | (ip(X) & ip(Y))) <=> ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X))))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(220,plain,
% 0.69/0.86 (![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (ip(X) & ip(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X)))))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[219])).
% 0.69/0.86 tff(221,plain,
% 0.69/0.86 (![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (ip(X) & ip(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (ip(X) & ip(Y)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(222,plain,
% 0.69/0.86 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_inverseOf, X, Y) => (ip(X) & ip(Y))) <=> ((~iext(uri_owl_inverseOf, X, Y)) | (ip(X) & ip(Y))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(223,plain,
% 0.69/0.86 (![X: $i, Y: $i] : (iext(uri_owl_inverseOf, X, Y) => (ip(X) & ip(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (ip(X) & ip(Y)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[222])).
% 0.69/0.86 tff(224,axiom,(![X: $i, Y: $i] : (iext(uri_owl_inverseOf, X, Y) => (ip(X) & ip(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_prop_inverseof_ext')).
% 0.69/0.86 tff(225,plain,
% 0.69/0.86 (![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (ip(X) & ip(Y)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.69/0.86 tff(226,plain,
% 0.69/0.86 (![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (ip(X) & ip(Y)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[225, 221])).
% 0.69/0.86 tff(227,plain,(
% 0.69/0.86 ![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (ip(X) & ip(Y)))),
% 0.69/0.86 inference(skolemize,[status(sab)],[226])).
% 0.69/0.86 tff(228,plain,
% 0.69/0.86 (![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X)))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[227, 220])).
% 0.69/0.86 tff(229,plain,
% 0.69/0.86 (![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X)))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[228, 218])).
% 0.69/0.86 tff(230,plain,
% 0.69/0.86 (((~![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X)))))) | ((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X)))))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(231,plain,
% 0.69/0.86 (((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) <=> ((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(232,plain,
% 0.69/0.86 (((~![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X)))))) | ((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X)))))) | ((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[231])).
% 0.69/0.86 tff(233,plain,
% 0.69/0.86 (((~![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X)))))) | ((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X)))))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))),
% 0.69/0.86 inference(transitivity,[status(thm)],[232, 230])).
% 0.69/0.86 tff(234,plain,
% 0.69/0.86 ((~![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X)))))) | ((~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(235,plain,
% 0.69/0.86 ((~![X: $i, Y: $i] : ((~iext(uri_owl_inverseOf, X, Y)) | (~((~ip(Y)) | (~ip(X)))))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.69/0.86 tff(236,plain,
% 0.69/0.86 (~((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[235, 229, 178])).
% 0.69/0.86 tff(237,plain,
% 0.69/0.86 (((~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))),
% 0.69/0.86 inference(tautology,[status(thm)],[])).
% 0.69/0.86 tff(238,plain,
% 0.69/0.86 (ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.69/0.86 tff(239,plain,
% 0.69/0.86 (((~icext(uri_ex_InversesOfFunctionalProperties, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.86 inference(tautology,[status(thm)],[])).
% 0.69/0.86 tff(240,plain,
% 0.69/0.86 (~icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[239, 168])).
% 0.69/0.86 tff(241,plain,
% 0.69/0.86 ((~(icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))),
% 0.69/0.86 inference(tautology,[status(thm)],[])).
% 0.69/0.86 tff(242,plain,
% 0.69/0.86 ((~(icext(uri_owl_InverseFunctionalProperty, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))))) | (~ip(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.69/0.86 tff(243,plain,
% 0.69/0.86 (~((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[242, 238, 216])).
% 0.69/0.86 tff(244,plain,
% 0.69/0.86 (((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.86 inference(tautology,[status(thm)],[])).
% 0.69/0.86 tff(245,plain,
% 0.69/0.86 (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.69/0.86 tff(246,plain,
% 0.69/0.86 ((~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.86 inference(tautology,[status(thm)],[])).
% 0.69/0.86 tff(247,plain,
% 0.69/0.86 ((~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))) | iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.69/0.87 tff(248,plain,
% 0.69/0.87 (iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[247, 185])).
% 0.69/0.87 tff(249,plain,
% 0.69/0.87 ((~![X: $i, Y: $i] : (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), X, Y) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), Y, X))) | (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(250,plain,
% 0.69/0.87 (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[249, 183])).
% 0.69/0.87 tff(251,plain,
% 0.69/0.87 (((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.87 inference(tautology,[status(thm)],[])).
% 0.69/0.87 tff(252,plain,
% 0.69/0.87 (iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[251, 243])).
% 0.69/0.87 tff(253,plain,
% 0.69/0.87 ((~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.87 inference(tautology,[status(thm)],[])).
% 0.69/0.87 tff(254,plain,
% 0.69/0.87 ((~(iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) <=> iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))) | iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[253, 252])).
% 0.69/0.87 tff(255,plain,
% 0.69/0.87 (iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[254, 250])).
% 0.69/0.87 tff(256,plain,
% 0.69/0.87 (^[P: $i] : rewrite((~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(257,plain,
% 0.69/0.87 (![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> ![P: $i] : (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))))))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[256])).
% 0.69/0.87 tff(258,plain,
% 0.69/0.87 (^[P: $i] : refl((~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(259,plain,
% 0.69/0.87 (![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[258])).
% 0.69/0.87 tff(260,plain,
% 0.69/0.87 (^[P: $i] : rewrite((~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(261,plain,
% 0.69/0.87 (![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[260])).
% 0.69/0.87 tff(262,plain,
% 0.69/0.87 (![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))),
% 0.69/0.87 inference(transitivity,[status(thm)],[261, 259])).
% 0.69/0.87 tff(263,plain,
% 0.69/0.87 (^[P: $i] : trans(monotonicity(rewrite(((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) <=> ((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))), trans(monotonicity(rewrite((~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)))) <=> (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))), ((icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P))))) <=> (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))), rewrite((icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))) <=> (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))), ((icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P))))) <=> (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))), ((((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)))))) <=> (((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))))), rewrite((((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) <=> (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))), ((((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)))))) <=> (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(264,plain,
% 0.69/0.87 (![P: $i] : (((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)))))) <=> ![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[263])).
% 0.69/0.87 tff(265,plain,
% 0.69/0.87 (^[P: $i] : rewrite((((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P))))))) <=> (((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)))))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(266,plain,
% 0.69/0.87 (![P: $i] : (((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P))))))) <=> ![P: $i] : (((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P))))))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[265])).
% 0.69/0.87 tff(267,plain,
% 0.69/0.87 (![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) <=> ![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2))))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(268,plain,
% 0.69/0.87 (^[P: $i] : rewrite((icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((iext(P, X, Y1) & iext(P, X, Y2)) => (Y1 = Y2)))) <=> (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(269,plain,
% 0.69/0.87 (![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((iext(P, X, Y1) & iext(P, X, Y2)) => (Y1 = Y2)))) <=> ![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2))))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[268])).
% 0.69/0.87 tff(270,axiom,(![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((iext(P, X, Y1) & iext(P, X, Y2)) => (Y1 = Y2))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_char_functional')).
% 0.69/0.87 tff(271,plain,
% 0.69/0.87 (![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2))))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.69/0.87 tff(272,plain,
% 0.69/0.87 (![P: $i] : (icext(uri_owl_FunctionalProperty, P) <=> (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2))))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[271, 267])).
% 0.69/0.87 tff(273,plain,(
% 0.69/0.87 ![P: $i] : (((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)))))))),
% 0.69/0.87 inference(skolemize,[status(sab)],[272])).
% 0.69/0.87 tff(274,plain,
% 0.69/0.87 (![P: $i] : (((~icext(uri_owl_FunctionalProperty, P)) | (ip(P) & ![X: $i, Y1: $i, Y2: $i] : ((~(iext(P, X, Y1) & iext(P, X, Y2))) | (Y1 = Y2)))) & (icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P)) & iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))) | (tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P))))))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[273, 266])).
% 0.69/0.87 tff(275,plain,
% 0.69/0.87 (![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[274, 264])).
% 0.69/0.87 tff(276,plain,
% 0.69/0.87 (![P: $i] : (~((~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2)))))))) | (~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P)))))))))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[275, 262])).
% 0.69/0.87 tff(277,plain,
% 0.69/0.87 (![P: $i] : (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))))))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[276, 257])).
% 0.69/0.87 tff(278,plain,
% 0.69/0.87 (((~![P: $i] : (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))))))) | (~((~(icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) = tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))))))) | (~((~(icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) = tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))))))))))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(279,plain,
% 0.69/0.87 ((~((~(icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) = tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))))))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))))))))) <=> (~((~(icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) = tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2))))))))))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(280,plain,
% 0.69/0.87 (((~![P: $i] : (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))))))) | (~((~(icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) = tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))))))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))))))) | (~((~(icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) = tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))))))))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[279])).
% 0.69/0.87 tff(281,plain,
% 0.69/0.87 (((~![P: $i] : (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))))))) | (~((~(icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) = tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))))))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))))))) | (~((~(icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) = tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))))))))))),
% 0.69/0.87 inference(transitivity,[status(thm)],[280, 278])).
% 0.69/0.87 tff(282,plain,
% 0.69/0.87 ((~![P: $i] : (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))))))) | (~((~(icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) = tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))))))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2))))))))))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(283,plain,
% 0.69/0.87 ((~![P: $i] : (~((~(icext(uri_owl_FunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_Y1_112(P) = tptp_fun_Y2_111(P)) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y1_112(P))) | (~iext(P, tptp_fun_X_113(P), tptp_fun_Y2_111(P))))))) | (~((~icext(uri_owl_FunctionalProperty, P)) | (~((~ip(P)) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(P, X, Y1)) | (~iext(P, X, Y2))))))))))) | (~((~(icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) = tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2))))))))))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.69/0.88 tff(284,plain,
% 0.69/0.88 (~((~(icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) = tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))))))))),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[283, 277])).
% 0.69/0.88 tff(285,plain,
% 0.69/0.88 (((~(icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) | (~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_X_113(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)), tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | (tptp_fun_Y1_112(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)) = tptp_fun_Y2_111(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))))))) | (~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2))))))))) | ((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))))))),
% 0.69/0.88 inference(tautology,[status(thm)],[])).
% 0.69/0.88 tff(286,plain,
% 0.69/0.88 ((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2))))))),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[285, 284])).
% 0.69/0.88 tff(287,plain,
% 0.69/0.88 (((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~iext(uri_owl_inverseOf, tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf)))) | icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(288,plain,
% 0.72/0.88 (icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[287, 176])).
% 0.72/0.88 tff(289,plain,
% 0.72/0.88 ((~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))))))) | (~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2))))))),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(290,plain,
% 0.72/0.88 ((~((~icext(uri_owl_FunctionalProperty, tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))))))) | (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2))))))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[289, 288])).
% 0.72/0.88 tff(291,plain,
% 0.72/0.88 (~((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[290, 286])).
% 0.72/0.88 tff(292,plain,
% 0.72/0.88 (((~ip(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf))) | (~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2))))) | ![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(293,plain,
% 0.72/0.88 (![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[292, 291])).
% 0.72/0.88 tff(294,plain,
% 0.72/0.88 (((~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~(tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))),
% 0.72/0.88 inference(tautology,[status(thm)],[])).
% 0.72/0.88 tff(295,plain,
% 0.72/0.88 (~(tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[294, 243])).
% 0.72/0.88 tff(296,plain,
% 0.72/0.88 (((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))) | ((tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))) <=> ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(297,plain,
% 0.72/0.88 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))) | ((tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(298,plain,
% 0.72/0.88 ((~![X: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y1)) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), X, Y2)))) | (tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)) = tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X1_116(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)))) | (~iext(tptp_fun_Y_42(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties), uri_owl_FunctionalProperty, uri_owl_inverseOf), tptp_fun_Y_114(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties)), tptp_fun_X2_115(tptp_fun_X_61(uri_owl_InverseFunctionalProperty, uri_ex_InversesOfFunctionalProperties))))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.72/0.90 tff(299,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[298, 295, 293, 255, 248])).
% 0.72/0.90 % SZS output end Proof
% 0.72/0.90 % E exiting
%------------------------------------------------------------------------------