%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB016+2 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:29:35 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWB016+2 : TPTP v9.0.0. Released v5.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 07:49:31 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(icext_type, type, (
% 0.12/0.38 icext: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_X_0_type, type, (
% 0.12/0.38 tptp_fun_X_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_X_2_type, type, (
% 0.12/0.38 tptp_fun_X_2: ( $i * $i ) > $i)).
% 0.12/0.38 tff(uri_owl_equivalentClass_type, type, (
% 0.12/0.38 uri_owl_equivalentClass: $i)).
% 0.12/0.38 tff(uri_rdfs_subClassOf_type, type, (
% 0.12/0.38 uri_rdfs_subClassOf: $i)).
% 0.12/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.38 tptp_fun_Y_1: ( $i * $i ) > $i)).
% 0.12/0.38 tff(ic_type, type, (
% 0.12/0.38 ic: $i > $o)).
% 0.12/0.38 tff(iext_type, type, (
% 0.12/0.38 iext: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(ip_type, type, (
% 0.12/0.38 ip: $i > $o)).
% 0.12/0.38 tff(uri_rdf_Property_type, type, (
% 0.12/0.38 uri_rdf_Property: $i)).
% 0.12/0.38 tff(uri_rdf_type_type, type, (
% 0.12/0.38 uri_rdf_type: $i)).
% 0.12/0.38 tff(uri_rdfs_Class_type, type, (
% 0.12/0.38 uri_rdfs_Class: $i)).
% 0.12/0.38 tff(uri_rdfs_domain_type, type, (
% 0.12/0.38 uri_rdfs_domain: $i)).
% 0.12/0.38 tff(uri_rdfs_subPropertyOf_type, type, (
% 0.12/0.38 uri_rdfs_subPropertyOf: $i)).
% 0.12/0.38 tff(tptp_fun_X_3_type, type, (
% 0.12/0.38 tptp_fun_X_3: ( $i * $i ) > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[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_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))))) <=> (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![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_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[C1: $i, C2: $i] : refl((~((~((~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_0(C2, C1))) | icext(C2, tptp_fun_X_0(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(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![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_0(C2, C1))) | icext(C2, tptp_fun_X_0(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(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (^[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_0(C2, C1))) | icext(C2, tptp_fun_X_0(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(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![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_0(C2, C1))) | icext(C2, tptp_fun_X_0(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(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![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_0(C2, C1))) | icext(C2, tptp_fun_X_0(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(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[6, 4])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (^[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(C1)) | (~ic(C2)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))), rewrite((iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1))))) <=> (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(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(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(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(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))))), 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_0(C2, C1))) | icext(C2, tptp_fun_X_0(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(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(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(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(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(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![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_0(C2, C1))) | icext(C2, tptp_fun_X_0(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(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (^[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_0(C2, C1))) | icext(C2, tptp_fun_X_0(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(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![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_0(C2, C1))) | icext(C2, tptp_fun_X_0(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(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.38 tff(15,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/sandbox/benchmark/theBenchmark.p','owl_rdfsext_subclassof')).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.38 tff(18,plain,(
% 0.12/0.38 ![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_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![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_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![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_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1))))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![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_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1))))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : ((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : ((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((~((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : ((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))))))) <=> (~((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : ((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : ((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : ((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : ((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : ((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[25, 23])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : ((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_0(C2, C1))) | icext(C2, tptp_fun_X_0(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : ((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (~((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : ((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : ((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))) | (iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (^[P: $i] : refl((iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P)) <=> (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P)) <=> ![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P)) <=> ![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(35,axiom,(![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rdf_type_ip')).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.39 tff(37,plain,(
% 0.20/0.39 ![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))),
% 0.20/0.39 inference(skolemize,[status(sab)],[36])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 ((~![P: $i] : (iext(uri_rdf_type, P, uri_rdf_Property) <=> ip(P))) | (iext(uri_rdf_type, uri_rdfs_subClassOf, uri_rdf_Property) <=> ip(uri_rdfs_subClassOf))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (iext(uri_rdf_type, uri_rdfs_subClassOf, uri_rdf_Property) <=> ip(uri_rdfs_subClassOf)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(44,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rdfs_cext_def')).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.39 tff(46,plain,(
% 0.20/0.39 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.20/0.39 inference(skolemize,[status(sab)],[45])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_rdfs_subClassOf, uri_rdf_Property) <=> icext(uri_rdf_Property, uri_rdfs_subClassOf))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (iext(uri_rdf_type, uri_rdfs_subClassOf, uri_rdf_Property) <=> icext(uri_rdf_Property, uri_rdfs_subClassOf)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.39 tff(50,assumption,(~icext(uri_rdf_Property, uri_rdfs_subClassOf)), introduced(assumption)).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (iext(uri_rdfs_domain, uri_rdfs_subClassOf, uri_rdfs_Class) <=> iext(uri_rdfs_domain, uri_rdfs_subClassOf, uri_rdfs_Class)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(52,axiom,(iext(uri_rdfs_domain, uri_rdfs_subClassOf, uri_rdfs_Class)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rdfs_subclassof_domain')).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (iext(uri_rdfs_domain, uri_rdfs_subClassOf, uri_rdfs_Class)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property) <=> iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(55,axiom,(iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rdfs_domain_domain')).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (^[P: $i, C: $i, X: $i, Y: $i] : refl((icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C))) <=> (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C))) <=> ![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (^[P: $i, C: $i, X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) <=> (~((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))), ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) <=> (~(~((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))))), rewrite((~(~((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))) <=> ((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y)))), ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) <=> ((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))))), (((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> (((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))) | icext(C, X)))), rewrite((((~iext(uri_rdfs_domain, P, C)) | (~iext(P, X, Y))) | icext(C, X)) <=> (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))), (((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> ![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)) <=> ![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (^[P: $i, C: $i, X: $i, Y: $i] : rewrite(((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) => icext(C, X)) <=> ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (![P: $i, C: $i, X: $i, Y: $i] : ((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) => icext(C, X)) <=> ![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.40 tff(64,axiom,(![P: $i, C: $i, X: $i, Y: $i] : ((iext(uri_rdfs_domain, P, C) & iext(P, X, Y)) => icext(C, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rdfs_domain_main')).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.20/0.40 tff(67,plain,(
% 0.20/0.40 ![P: $i, C: $i, X: $i, Y: $i] : ((~(iext(uri_rdfs_domain, P, C) & iext(P, X, Y))) | icext(C, X))),
% 0.20/0.40 inference(skolemize,[status(sab)],[66])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))) | (icext(uri_rdf_Property, uri_rdfs_subClassOf) | (~iext(uri_rdfs_domain, uri_rdfs_subClassOf, uri_rdfs_Class)) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)))) <=> ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))) | icext(uri_rdf_Property, uri_rdfs_subClassOf) | (~iext(uri_rdfs_domain, uri_rdfs_subClassOf, uri_rdfs_Class)) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))) | (icext(uri_rdf_Property, uri_rdfs_subClassOf) | (~iext(uri_rdfs_domain, uri_rdfs_subClassOf, uri_rdfs_Class)) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 ((~![P: $i, C: $i, X: $i, Y: $i] : (icext(C, X) | (~iext(P, X, Y)) | (~iext(uri_rdfs_domain, P, C)))) | icext(uri_rdf_Property, uri_rdfs_subClassOf) | (~iext(uri_rdfs_domain, uri_rdfs_subClassOf, uri_rdfs_Class)) | (~iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[72, 69, 56, 53, 50])).
% 0.20/0.40 tff(74,plain,(icext(uri_rdf_Property, uri_rdfs_subClassOf)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 ((~(iext(uri_rdf_type, uri_rdfs_subClassOf, uri_rdf_Property) <=> icext(uri_rdf_Property, uri_rdfs_subClassOf))) | iext(uri_rdf_type, uri_rdfs_subClassOf, uri_rdf_Property) | (~icext(uri_rdf_Property, uri_rdfs_subClassOf))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 ((~(iext(uri_rdf_type, uri_rdfs_subClassOf, uri_rdf_Property) <=> icext(uri_rdf_Property, uri_rdfs_subClassOf))) | iext(uri_rdf_type, uri_rdfs_subClassOf, uri_rdf_Property)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (iext(uri_rdf_type, uri_rdfs_subClassOf, uri_rdf_Property)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[76, 49])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 ((~(iext(uri_rdf_type, uri_rdfs_subClassOf, uri_rdf_Property) <=> ip(uri_rdfs_subClassOf))) | (~iext(uri_rdf_type, uri_rdfs_subClassOf, uri_rdf_Property)) | ip(uri_rdfs_subClassOf)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 ((~(iext(uri_rdf_type, uri_rdfs_subClassOf, uri_rdf_Property) <=> ip(uri_rdfs_subClassOf))) | ip(uri_rdfs_subClassOf)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (ip(uri_rdfs_subClassOf)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[79, 40])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))))) <=> (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (^[P1: $i, P2: $i] : refl((~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))))) <=> (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))))) <=> (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[86, 84])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (^[P1: $i, P2: $i] : trans(monotonicity(rewrite(((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) <=> ((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))), rewrite((iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))))) <=> (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))), ((((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) <=> (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))))), rewrite((((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) <=> (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))))))))), ((((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) <=> (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 (^[P1: $i, P2: $i] : rewrite((((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))))))) <=> (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))))))) <=> ![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) <=> ![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 (^[P1: $i, P2: $i] : rewrite((iext(uri_rdfs_subPropertyOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) => iext(P2, X, Y)))) <=> (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) => iext(P2, X, Y)))) <=> ![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.40 tff(95,axiom,(![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) => iext(P2, X, Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_rdfsext_subpropertyof')).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.20/0.40 tff(98,plain,(
% 0.20/0.40 ![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[97])).
% 0.20/0.40 tff(99,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.20/0.40 tff(101,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[100, 87])).
% 0.20/0.40 tff(102,plain,
% 0.20/0.40 (![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[101, 82])).
% 0.20/0.40 tff(103,plain,
% 0.20/0.40 (((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_rdfs_subClassOf)) | (~ip(uri_owl_equivalentClass)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)) | (~((~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | iext(uri_rdfs_subClassOf, X, Y)))))))))) <=> ((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_rdfs_subClassOf)) | (~ip(uri_owl_equivalentClass)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)) | (~((~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | iext(uri_rdfs_subClassOf, X, Y))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 ((~((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)) | (~((~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | iext(uri_rdfs_subClassOf, X, Y))))))))) <=> (~((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_rdfs_subClassOf)) | (~ip(uri_owl_equivalentClass)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)) | (~((~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | iext(uri_rdfs_subClassOf, X, Y)))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)) | (~((~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | iext(uri_rdfs_subClassOf, X, Y)))))))))) <=> ((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_rdfs_subClassOf)) | (~ip(uri_owl_equivalentClass)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)) | (~((~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | iext(uri_rdfs_subClassOf, X, Y))))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[104])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)) | (~((~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | iext(uri_rdfs_subClassOf, X, Y)))))))))) <=> ((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_rdfs_subClassOf)) | (~ip(uri_owl_equivalentClass)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)) | (~((~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | iext(uri_rdfs_subClassOf, X, Y))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[105, 103])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 ((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)) | (~((~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | iext(uri_rdfs_subClassOf, X, Y)))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 ((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1))) | iext(P2, tptp_fun_X_2(P2, P1), tptp_fun_Y_1(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P1)) | (~ip(P2)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_rdfs_subClassOf)) | (~ip(uri_owl_equivalentClass)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)) | (~((~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | iext(uri_rdfs_subClassOf, X, Y)))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (~((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_rdfs_subClassOf)) | (~ip(uri_owl_equivalentClass)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)) | (~((~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | iext(uri_rdfs_subClassOf, X, Y))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[108, 102])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_rdfs_subClassOf)) | (~ip(uri_owl_equivalentClass)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)) | (~((~ip(uri_owl_equivalentClass)) | (~ip(uri_rdfs_subClassOf)) | (~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | iext(uri_rdfs_subClassOf, X, Y)))))))) | (iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_rdfs_subClassOf)) | (~ip(uri_owl_equivalentClass)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_rdfs_subClassOf)) | (~ip(uri_owl_equivalentClass)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 ((~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)) <=> (~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(113,axiom,(~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_conclusion_fullish_016_Reflective_Tautologies_II')).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (~iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 (ip(uri_owl_equivalentClass) <=> ip(uri_owl_equivalentClass)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(116,axiom,(ip(uri_owl_equivalentClass)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_prop_equivalentclass_type')).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (ip(uri_owl_equivalentClass)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 ((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_rdfs_subClassOf)) | (~ip(uri_owl_equivalentClass)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_rdfs_subClassOf)) | (~ip(uri_owl_equivalentClass)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 ((~(iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) | (~ip(uri_rdfs_subClassOf)) | (~ip(uri_owl_equivalentClass)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))) | (~ip(uri_rdfs_subClassOf)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[118, 117, 114])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 ((~ip(uri_rdfs_subClassOf)) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[119, 111])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[120, 80])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 (((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 (iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(X)) | (~ic(Y))))) <=> ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(X)) | (~ic(Y))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (![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)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 (^[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))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 (![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)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(129,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.41 tff(131,axiom,(![X: $i, Y: $i] : (iext(uri_owl_equivalentClass, X, Y) => (ic(X) & ic(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_prop_equivalentclass_ext')).
% 0.20/0.41 tff(132,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.41 tff(133,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.20/0.41 tff(134,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (ic(X) & ic(Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[133])).
% 0.20/0.41 tff(135,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(X)) | (~ic(Y)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.20/0.41 tff(136,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(X)) | (~ic(Y)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[135, 125])).
% 0.20/0.41 tff(137,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(X)) | (~ic(Y)))))) | ((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(X)) | (~ic(Y)))))) | (~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(138,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(X)) | (~ic(Y)))))) | ((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(139,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : ((~iext(uri_owl_equivalentClass, X, Y)) | (~((~ic(X)) | (~ic(Y)))))) | (~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.41 tff(140,plain,
% 0.20/0.41 (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[139, 136, 123])).
% 0.20/0.41 tff(141,plain,
% 0.20/0.41 (((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(142,plain,
% 0.20/0.41 (ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.20/0.41 tff(143,plain,
% 0.20/0.41 (((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(144,plain,
% 0.20/0.41 (ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[143, 140])).
% 0.20/0.41 tff(145,plain,
% 0.20/0.41 (((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(146,plain,
% 0.20/0.42 (~iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[145, 121])).
% 0.20/0.42 tff(147,plain,
% 0.20/0.42 ((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(148,plain,
% 0.20/0.42 ((~(iext(uri_rdfs_subClassOf, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.20/0.42 tff(149,plain,
% 0.20/0.42 (~((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[148, 144, 142, 31])).
% 0.20/0.42 tff(150,plain,
% 0.20/0.42 (((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | (~icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(151,plain,
% 0.20/0.42 (~icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.20/0.42 tff(152,plain,
% 0.20/0.42 (((~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(153,plain,
% 0.20/0.42 (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[152, 149])).
% 0.20/0.42 tff(154,plain,
% 0.20/0.42 ((~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))) | (~icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))) | icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(155,plain,
% 0.20/0.42 (~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[154, 153, 151])).
% 0.20/0.42 tff(156,plain,
% 0.20/0.42 (^[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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))) <=> (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(157,plain,
% 0.20/0.42 (![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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.42 tff(158,plain,
% 0.20/0.42 (^[C1: $i, C2: $i] : refl((~((~((~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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(159,plain,
% 0.20/0.42 (![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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[158])).
% 0.20/0.42 tff(160,plain,
% 0.20/0.42 (^[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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(161,plain,
% 0.20/0.42 (![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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[160])).
% 0.20/0.42 tff(162,plain,
% 0.20/0.42 (![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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[161, 159])).
% 0.20/0.42 tff(163,plain,
% 0.20/0.42 (^[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(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))), trans(monotonicity(rewrite((~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))) <=> (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))), rewrite((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))), ((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))), 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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(164,plain,
% 0.20/0.42 (![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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[163])).
% 0.20/0.42 tff(165,plain,
% 0.20/0.42 (^[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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(166,plain,
% 0.20/0.42 (![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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(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(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.42 tff(167,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(168,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(169,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[168])).
% 0.20/0.42 tff(170,axiom,(![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_eqdis_equivalentclass')).
% 0.20/0.42 tff(171,plain,
% 0.20/0.42 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.20/0.42 tff(172,plain,
% 0.20/0.42 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.20/0.42 tff(173,plain,(
% 0.20/0.42 ![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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[172])).
% 0.20/0.42 tff(174,plain,
% 0.20/0.42 (![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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[173, 166])).
% 0.20/0.42 tff(175,plain,
% 0.20/0.42 (![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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[174, 164])).
% 0.20/0.42 tff(176,plain,
% 0.20/0.42 (![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_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[175, 162])).
% 0.20/0.42 tff(177,plain,
% 0.20/0.42 (![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[176, 157])).
% 0.20/0.42 tff(178,plain,
% 0.20/0.42 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(179,plain,
% 0.20/0.43 ((~((~(iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))))))) <=> (~((~(iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(180,plain,
% 0.20/0.43 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.43 tff(181,plain,
% 0.20/0.43 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[180, 178])).
% 0.20/0.43 tff(182,plain,
% 0.20/0.43 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(183,plain,
% 0.20/0.43 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_3(C2, C1)) <=> icext(C2, tptp_fun_X_3(C2, C1)))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C1)) | (~ic(C2)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.43 tff(184,plain,
% 0.20/0.43 (~((~(iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[183, 177])).
% 0.20/0.43 tff(185,plain,
% 0.20/0.43 (((~(iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass)) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~(icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_3(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))))) | (~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))))) | ((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(186,plain,
% 0.20/0.44 ((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.20/0.44 tff(187,plain,
% 0.20/0.44 ((~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))))) | (~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(188,plain,
% 0.20/0.44 ((~((~iext(uri_owl_equivalentClass, tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))))) | (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[187, 123])).
% 0.20/0.44 tff(189,plain,
% 0.20/0.44 (~((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[188, 186])).
% 0.20/0.44 tff(190,plain,
% 0.20/0.44 (((~ic(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~ic(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass))) | (~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X)))) | ![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(191,plain,
% 0.20/0.44 (![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.20/0.44 tff(192,plain,
% 0.20/0.44 ((~![X: $i] : (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), X) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), X))) | (icext(tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))) <=> icext(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_0(tptp_fun_Y_1(uri_rdfs_subClassOf, uri_owl_equivalentClass), tptp_fun_X_2(uri_rdfs_subClassOf, uri_owl_equivalentClass))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(193,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[192, 191, 155])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------