%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB027+2 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:41 AM UTC 2025
% Result : Theorem 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWB027+2 : TPTP v9.0.0. Released v5.2.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 07:52:54 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 tff(tptp_fun_X2_4_type, type, (
% 0.19/0.52 tptp_fun_X2_4: $i > $i)).
% 0.19/0.52 tff(uri_ex_p_type, type, (
% 0.19/0.52 uri_ex_p: $i)).
% 0.19/0.52 tff(tptp_fun_X1_5_type, type, (
% 0.19/0.52 tptp_fun_X1_5: $i > $i)).
% 0.19/0.52 tff(iext_type, type, (
% 0.19/0.52 iext: ( $i * $i * $i ) > $o)).
% 0.19/0.52 tff(uri_owl_sameAs_type, type, (
% 0.19/0.52 uri_owl_sameAs: $i)).
% 0.19/0.52 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.52 tptp_fun_Y_3: $i > $i)).
% 0.19/0.52 tff(tptp_fun_BNODE_v_8_type, type, (
% 0.19/0.52 tptp_fun_BNODE_v_8: $i)).
% 0.19/0.52 tff(ip_type, type, (
% 0.19/0.52 ip: $i > $o)).
% 0.19/0.52 tff(uri_owl_inverseOf_type, type, (
% 0.19/0.52 uri_owl_inverseOf: $i)).
% 0.19/0.52 tff(tptp_fun_X_7_type, type, (
% 0.19/0.52 tptp_fun_X_7: ( $i * $i ) > $i)).
% 0.19/0.52 tff(tptp_fun_Y_6_type, type, (
% 0.19/0.52 tptp_fun_Y_6: ( $i * $i ) > $i)).
% 0.19/0.52 tff(uri_rdf_nil_type, type, (
% 0.19/0.52 uri_rdf_nil: $i)).
% 0.19/0.52 tff(tptp_fun_BNODE_l2_9_type, type, (
% 0.19/0.52 tptp_fun_BNODE_l2_9: $i)).
% 0.19/0.52 tff(uri_rdf_rest_type, type, (
% 0.19/0.52 uri_rdf_rest: $i)).
% 0.19/0.52 tff(uri_rdf_first_type, type, (
% 0.19/0.52 uri_rdf_first: $i)).
% 0.19/0.52 tff(tptp_fun_BNODE_l1_10_type, type, (
% 0.19/0.52 tptp_fun_BNODE_l1_10: $i)).
% 0.19/0.52 tff(uri_owl_propertyChainAxiom_type, type, (
% 0.19/0.52 uri_owl_propertyChainAxiom: $i)).
% 0.19/0.52 tff(icext_type, type, (
% 0.19/0.52 icext: ( $i * $i ) > $o)).
% 0.19/0.52 tff(uri_owl_InverseFunctionalProperty_type, type, (
% 0.19/0.52 uri_owl_InverseFunctionalProperty: $i)).
% 0.19/0.52 tff(tptp_fun_Y2_0_type, type, (
% 0.19/0.52 tptp_fun_Y2_0: ( $i * $i * $i ) > $i)).
% 0.19/0.52 tff(tptp_fun_Y0_2_type, type, (
% 0.19/0.52 tptp_fun_Y0_2: ( $i * $i * $i ) > $i)).
% 0.19/0.52 tff(tptp_fun_Y1_1_type, type, (
% 0.19/0.52 tptp_fun_Y1_1: ( $i * $i * $i ) > $i)).
% 0.19/0.52 tff(uri_rdf_type_type, type, (
% 0.19/0.52 uri_rdf_type: $i)).
% 0.19/0.52 tff(1,plain,
% 0.19/0.52 (^[X: $i, Y: $i] : refl((iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> (iext(uri_owl_sameAs, X, Y) <=> (X = Y)))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(2,plain,
% 0.19/0.52 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.52 tff(3,plain,
% 0.19/0.52 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(4,axiom,(![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_eqdis_sameas')).
% 0.19/0.52 tff(5,plain,
% 0.19/0.52 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.52 tff(6,plain,(
% 0.19/0.52 ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.52 inference(skolemize,[status(sab)],[5])).
% 0.19/0.52 tff(7,plain,
% 0.19/0.52 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.52 tff(8,plain,
% 0.19/0.52 ((~![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))) | (iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p)) <=> (tptp_fun_X2_4(uri_ex_p) = tptp_fun_X1_5(uri_ex_p)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(9,plain,
% 0.19/0.52 (iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p)) <=> (tptp_fun_X2_4(uri_ex_p) = tptp_fun_X1_5(uri_ex_p))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.52 tff(10,plain,
% 0.19/0.52 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))) <=> (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(11,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.52 tff(12,plain,
% 0.19/0.52 (^[P1: $i, P2: $i] : refl((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(13,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.52 tff(14,plain,
% 0.19/0.52 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(15,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.52 tff(16,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[15, 13])).
% 0.19/0.52 tff(17,plain,
% 0.19/0.52 (^[P1: $i, P2: $i] : trans(monotonicity(rewrite(((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))), trans(monotonicity(rewrite((~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))) <=> (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))), ((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))), rewrite((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))), ((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))), ((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) <=> (((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))), rewrite((((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))))), ((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(18,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.52 tff(19,plain,
% 0.19/0.52 (^[P1: $i, P2: $i] : rewrite((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))) <=> (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(20,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))) <=> ![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.52 tff(21,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(22,plain,
% 0.19/0.52 (^[P1: $i, P2: $i] : rewrite((iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(23,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.52 tff(24,axiom,(![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_inv')).
% 0.19/0.52 tff(25,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.52 tff(26,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.52 tff(27,plain,(
% 0.19/0.52 ![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))))),
% 0.19/0.52 inference(skolemize,[status(sab)],[26])).
% 0.19/0.52 tff(28,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.52 tff(29,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.52 tff(30,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.19/0.52 tff(31,plain,
% 0.19/0.52 (![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[30, 11])).
% 0.19/0.52 tff(32,plain,
% 0.19/0.52 (((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~(iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8)) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8)))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))))))) <=> ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~(iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8)) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8)))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(33,plain,
% 0.19/0.52 ((~((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8)) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8)))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))))))) <=> (~((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~(iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8)) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8)))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(34,plain,
% 0.19/0.52 (((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8)) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8)))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))))))) <=> ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~(iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8)) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8)))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.52 tff(35,plain,
% 0.19/0.52 (((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8)) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8)))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))))))) <=> ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~(iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8)) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8)))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[34, 32])).
% 0.19/0.52 tff(36,plain,
% 0.19/0.52 ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8)) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8)))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(37,plain,
% 0.19/0.52 ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_7(P2, P1), tptp_fun_Y_6(P2, P1)) <=> iext(P2, tptp_fun_Y_6(P2, P1), tptp_fun_X_7(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~(iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8)) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8)))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.52 tff(38,plain,
% 0.19/0.52 (~((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~(iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8)) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8)))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[37, 31])).
% 0.19/0.52 tff(39,plain,
% 0.19/0.52 (((~(iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p) | (~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~(iext(BNODE_v!8, tptp_fun_X_7(uri_ex_p, BNODE_v!8), tptp_fun_Y_6(uri_ex_p, BNODE_v!8)) <=> iext(uri_ex_p, tptp_fun_Y_6(uri_ex_p, BNODE_v!8), tptp_fun_X_7(uri_ex_p, BNODE_v!8)))))) | (~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))))) | ((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(40,plain,
% 0.19/0.52 ((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.52 tff(41,plain,
% 0.19/0.52 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p)) <=> ?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(42,plain,
% 0.19/0.52 (^[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2))), ((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) <=> ((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v))), ((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v)))), (((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> ((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil))), (((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)))), ((((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p)) <=> ((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))), ((((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p)) <=> (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(43,plain,
% 0.19/0.52 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p)) <=> ?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.52 tff(44,axiom,(?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (((((iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p)) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2)) & iext(uri_rdf_first, BNODE_l2, BNODE_v)) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_premise_fullish_027_Inferred_Property_Characteristics_II')).
% 0.19/0.52 tff(45,plain,
% 0.19/0.52 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.52 tff(46,plain,
% 0.19/0.52 (?[BNODE_l1: $i, BNODE_l2: $i, BNODE_v: $i] : (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1) & iext(uri_rdf_first, BNODE_l1, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1, BNODE_l2) & iext(uri_rdf_first, BNODE_l2, BNODE_v) & iext(uri_rdf_rest, BNODE_l2, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v, uri_ex_p))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.52 tff(47,plain,(
% 0.19/0.52 iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) & iext(uri_rdf_first, BNODE_l1!10, uri_ex_p) & iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9) & iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8) & iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)),
% 0.19/0.52 inference(skolemize,[status(sab)],[46])).
% 0.19/0.52 tff(48,plain,
% 0.19/0.52 (iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)),
% 0.19/0.52 inference(and_elim,[status(thm)],[47])).
% 0.19/0.52 tff(49,plain,
% 0.19/0.52 ((~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))))) | (~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(50,plain,
% 0.19/0.52 ((~((~iext(uri_owl_inverseOf, BNODE_v!8, uri_ex_p)) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))))) | (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.52 tff(51,plain,
% 0.19/0.52 (~((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[50, 40])).
% 0.19/0.52 tff(52,plain,
% 0.19/0.52 (((~ip(BNODE_v!8)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X)))) | ![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(53,plain,
% 0.19/0.52 (![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.52 tff(54,plain,
% 0.19/0.52 ((~![X: $i, Y: $i] : (iext(BNODE_v!8, X, Y) <=> iext(uri_ex_p, Y, X))) | (iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p)) <=> iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(55,plain,
% 0.19/0.52 (iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p)) <=> iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.19/0.52 tff(56,plain,
% 0.19/0.52 (^[P: $i] : rewrite((~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(57,plain,
% 0.19/0.53 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> ![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.53 tff(58,plain,
% 0.19/0.53 (^[P: $i] : refl((~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(59,plain,
% 0.19/0.53 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.53 tff(60,plain,
% 0.19/0.53 (^[P: $i] : rewrite((~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(61,plain,
% 0.19/0.53 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.53 tff(62,plain,
% 0.19/0.53 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[61, 59])).
% 0.19/0.53 tff(63,plain,
% 0.19/0.53 (^[P: $i] : trans(monotonicity(rewrite(((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) <=> ((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))), trans(monotonicity(rewrite((~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P)))) <=> (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))), ((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))), rewrite((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))), ((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))), ((((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P)))))) <=> (((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))))), rewrite((((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))), ((((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P)))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(64,plain,
% 0.19/0.53 (![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P)))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.53 tff(65,plain,
% 0.19/0.53 (^[P: $i] : rewrite((((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P))))))) <=> (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P)))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(66,plain,
% 0.19/0.53 (![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P))))))) <=> ![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.53 tff(67,plain,
% 0.19/0.53 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) <=> ![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(68,plain,
% 0.19/0.53 (^[P: $i] : rewrite((icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((iext(P, X1, Y) & iext(P, X2, Y)) => (X1 = X2)))) <=> (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(69,plain,
% 0.19/0.53 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((iext(P, X1, Y) & iext(P, X2, Y)) => (X1 = X2)))) <=> ![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.53 tff(70,axiom,(![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((iext(P, X1, Y) & iext(P, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_char_inversefunctional')).
% 0.19/0.53 tff(71,plain,
% 0.19/0.53 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.53 tff(72,plain,
% 0.19/0.53 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.53 tff(73,plain,(
% 0.19/0.53 ![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P)))))))),
% 0.19/0.53 inference(skolemize,[status(sab)],[72])).
% 0.19/0.53 tff(74,plain,
% 0.19/0.53 (![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P)) & iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))) | (tptp_fun_X1_5(P) = tptp_fun_X2_4(P))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.53 tff(75,plain,
% 0.19/0.53 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.19/0.53 tff(76,plain,
% 0.19/0.53 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P)))))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[75, 62])).
% 0.19/0.53 tff(77,plain,
% 0.19/0.53 (![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[76, 57])).
% 0.19/0.53 tff(78,plain,
% 0.19/0.53 (((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(79,plain,
% 0.19/0.53 ((~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))) <=> (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(80,plain,
% 0.19/0.53 (((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[79])).
% 0.19/0.53 tff(81,plain,
% 0.19/0.53 (((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[80, 78])).
% 0.19/0.53 tff(82,plain,
% 0.19/0.53 ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(83,plain,
% 0.19/0.53 ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_5(P) = tptp_fun_X2_4(P)) | (~iext(P, tptp_fun_X1_5(P), tptp_fun_Y_3(P))) | (~iext(P, tptp_fun_X2_4(P), tptp_fun_Y_3(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.53 tff(84,plain,
% 0.19/0.53 (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[83, 77])).
% 0.19/0.53 tff(85,plain,
% 0.19/0.53 (((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))) | (icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(86,plain,
% 0.19/0.53 (icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.53 tff(87,plain,
% 0.19/0.53 (iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)),
% 0.19/0.53 inference(and_elim,[status(thm)],[47])).
% 0.19/0.53 tff(88,plain,
% 0.19/0.53 (iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)),
% 0.19/0.53 inference(and_elim,[status(thm)],[47])).
% 0.19/0.53 tff(89,plain,
% 0.19/0.53 (iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)),
% 0.19/0.53 inference(and_elim,[status(thm)],[47])).
% 0.19/0.53 tff(90,plain,
% 0.19/0.53 (iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)),
% 0.19/0.53 inference(and_elim,[status(thm)],[47])).
% 0.19/0.53 tff(91,plain,
% 0.19/0.53 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))))))), (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))))))))), rewrite(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))), (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(92,plain,
% 0.19/0.53 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.53 tff(93,plain,
% 0.19/0.53 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : refl(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(94,plain,
% 0.19/0.53 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.53 tff(95,plain,
% 0.19/0.53 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : rewrite(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(96,plain,
% 0.19/0.53 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.53 tff(97,plain,
% 0.19/0.53 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.53 tff(98,plain,
% 0.19/0.53 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) <=> ((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))), trans(monotonicity(rewrite((~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) <=> (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))) <=> (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))), rewrite((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) <=> (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))))), rewrite((((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(99,plain,
% 0.19/0.54 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.54 tff(100,plain,
% 0.19/0.54 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : rewrite(((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(101,plain,
% 0.19/0.54 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[100])).
% 0.19/0.54 tff(102,plain,
% 0.19/0.54 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(103,plain,
% 0.19/0.54 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2))), ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))), ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2)))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))), (((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2))))) <=> ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))))), rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))), (((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(104,plain,
% 0.19/0.54 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[103])).
% 0.19/0.54 tff(105,axiom,(![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_chain_002')).
% 0.19/0.54 tff(106,plain,
% 0.19/0.54 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.54 tff(107,plain,
% 0.19/0.54 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.19/0.54 tff(108,plain,(
% 0.19/0.54 ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))),
% 0.19/0.54 inference(skolemize,[status(sab)],[107])).
% 0.19/0.54 tff(109,plain,
% 0.19/0.54 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.19/0.54 tff(110,plain,
% 0.19/0.54 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[109, 99])).
% 0.19/0.54 tff(111,plain,
% 0.19/0.54 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[110, 97])).
% 0.19/0.54 tff(112,plain,
% 0.19/0.54 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[111, 92])).
% 0.19/0.54 tff(113,plain,
% 0.19/0.54 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~((~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~((~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)))))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(114,plain,
% 0.19/0.54 (((~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~((~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p))))))))) <=> ((~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~((~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)))))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(115,plain,
% 0.19/0.54 ((~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~((~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p))))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(116,plain,
% 0.19/0.54 (((~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~((~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)))))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[115])).
% 0.19/0.54 tff(117,plain,
% 0.19/0.54 (((~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2))))))))))) <=> ((~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~((~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)))))))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[116, 114])).
% 0.19/0.54 tff(118,plain,
% 0.19/0.54 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~((~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p))))))))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.55 tff(119,plain,
% 0.19/0.55 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~((~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)))))))))),
% 0.19/0.55 inference(transitivity,[status(thm)],[118, 113])).
% 0.19/0.55 tff(120,plain,
% 0.19/0.55 ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~(iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~ip(BNODE_v!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))))))))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(121,plain,
% 0.19/0.55 ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_rest, BNODE_l2!9, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l2!9, BNODE_v!8)) | (~iext(uri_rdf_rest, BNODE_l1!10, BNODE_l2!9)) | (~iext(uri_rdf_first, BNODE_l1!10, uri_ex_p)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~((~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p))))))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.55 tff(122,plain,
% 0.19/0.55 (~((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~((~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)))))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[121, 112, 90, 89, 88, 87])).
% 0.19/0.55 tff(123,plain,
% 0.19/0.55 (((~(iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)) | (~((~iext(BNODE_v!8, tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | (~iext(uri_ex_p, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y1_1(BNODE_v!8, uri_ex_p, uri_owl_sameAs))) | iext(uri_owl_sameAs, tptp_fun_Y0_2(BNODE_v!8, uri_ex_p, uri_owl_sameAs), tptp_fun_Y2_0(BNODE_v!8, uri_ex_p, uri_owl_sameAs)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p))))))) | ((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)))))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(124,plain,
% 0.19/0.55 ((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.19/0.55 tff(125,plain,
% 0.19/0.55 (iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)),
% 0.19/0.55 inference(and_elim,[status(thm)],[47])).
% 0.19/0.55 tff(126,plain,
% 0.19/0.55 ((~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)))))) | (~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p))))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(127,plain,
% 0.19/0.55 ((~((~iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, BNODE_l1!10)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)))))) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.19/0.55 tff(128,plain,
% 0.19/0.55 (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[127, 124])).
% 0.19/0.55 tff(129,plain,
% 0.19/0.55 (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p))) | ip(uri_ex_p)),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(130,plain,
% 0.19/0.55 (ip(uri_ex_p)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.19/0.55 tff(131,plain,
% 0.19/0.55 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(132,plain,
% 0.19/0.55 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[131])).
% 0.19/0.55 tff(133,plain,
% 0.19/0.55 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(134,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rdfs_cext_def')).
% 0.19/0.55 tff(135,plain,
% 0.19/0.55 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.55 tff(136,plain,(
% 0.19/0.55 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.55 inference(skolemize,[status(sab)],[135])).
% 0.19/0.55 tff(137,plain,
% 0.19/0.55 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.19/0.55 tff(138,plain,
% 0.19/0.55 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(139,plain,
% 0.19/0.55 (iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.19/0.55 tff(140,plain,
% 0.19/0.55 ((~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)) <=> (~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(141,axiom,(~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_conclusion_fullish_027_Inferred_Property_Characteristics_II')).
% 0.19/0.55 tff(142,plain,
% 0.19/0.55 (~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.55 tff(143,plain,
% 0.19/0.55 ((~(iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))) | iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) | (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(144,plain,
% 0.19/0.55 ((~(iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))) | (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.19/0.55 tff(145,plain,
% 0.19/0.55 (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[144, 139])).
% 0.19/0.55 tff(146,plain,
% 0.19/0.55 ((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))))) | icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p))))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(147,plain,
% 0.19/0.55 ((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))))) | (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[146, 145, 130])).
% 0.19/0.55 tff(148,plain,
% 0.19/0.55 (~((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[147, 86])).
% 0.19/0.55 tff(149,plain,
% 0.19/0.55 (((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p))) | iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(150,plain,
% 0.19/0.55 (iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.19/0.55 tff(151,plain,
% 0.19/0.55 ((~(iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p)) <=> iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))) | iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(152,plain,
% 0.19/0.55 ((~(iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p)) <=> iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p)))) | iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.19/0.55 tff(153,plain,
% 0.19/0.55 (iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[152, 55])).
% 0.19/0.55 tff(154,plain,
% 0.19/0.55 (((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p))) | iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(155,plain,
% 0.19/0.55 (iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[154, 148])).
% 0.19/0.55 tff(156,plain,
% 0.19/0.55 (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~ip(BNODE_v!8)) | (~ip(uri_owl_sameAs)) | (~ip(uri_ex_p))) | ![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(157,plain,
% 0.19/0.55 (![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[156, 128])).
% 0.19/0.55 tff(158,plain,
% 0.19/0.55 (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | ((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p))) | iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p))) | iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(159,plain,
% 0.19/0.55 ((iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p)))) <=> ((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p))) | iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(160,plain,
% 0.19/0.55 (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p))))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | ((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p))) | iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p))))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[159])).
% 0.19/0.55 tff(161,plain,
% 0.19/0.55 (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p))))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p))) | iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p)))),
% 0.19/0.55 inference(transitivity,[status(thm)],[160, 158])).
% 0.19/0.55 tff(162,plain,
% 0.19/0.55 ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(163,plain,
% 0.19/0.55 ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_owl_sameAs, Y0, Y2) | (~iext(uri_ex_p, Y0, Y1)) | (~iext(BNODE_v!8, Y1, Y2)))) | (~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(BNODE_v!8, tptp_fun_Y_3(uri_ex_p), tptp_fun_X1_5(uri_ex_p))) | iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.19/0.55 tff(164,plain,
% 0.19/0.55 (iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[163, 157, 155, 153])).
% 0.19/0.55 tff(165,plain,
% 0.19/0.55 ((~(iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p)) <=> (tptp_fun_X2_4(uri_ex_p) = tptp_fun_X1_5(uri_ex_p)))) | (~iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p))) | (tptp_fun_X2_4(uri_ex_p) = tptp_fun_X1_5(uri_ex_p))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(166,plain,
% 0.19/0.55 ((~(iext(uri_owl_sameAs, tptp_fun_X2_4(uri_ex_p), tptp_fun_X1_5(uri_ex_p)) <=> (tptp_fun_X2_4(uri_ex_p) = tptp_fun_X1_5(uri_ex_p)))) | (tptp_fun_X2_4(uri_ex_p) = tptp_fun_X1_5(uri_ex_p))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.19/0.55 tff(167,plain,
% 0.19/0.55 (tptp_fun_X2_4(uri_ex_p) = tptp_fun_X1_5(uri_ex_p)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[166, 9])).
% 0.19/0.55 tff(168,plain,
% 0.19/0.55 (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)),
% 0.19/0.55 inference(symmetry,[status(thm)],[167])).
% 0.19/0.55 tff(169,plain,
% 0.19/0.55 (((~iext(uri_ex_p, tptp_fun_X2_4(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_5(uri_ex_p), tptp_fun_Y_3(uri_ex_p))) | (tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p))) | (~(tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p)))),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(170,plain,
% 0.19/0.55 (~(tptp_fun_X1_5(uri_ex_p) = tptp_fun_X2_4(uri_ex_p))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[169, 148])).
% 0.19/0.55 tff(171,plain,
% 0.19/0.55 ($false),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[170, 168])).
% 0.19/0.55 % SZS output end Proof
% 0.19/0.55 % E exiting
%------------------------------------------------------------------------------