%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB042+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:29:44 AM UTC 2025
% Result : Theorem 0.63s 0.80s
% Output : Proof 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWB042+1 : TPTP v9.0.0. Released v5.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 07:53:33 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.63/0.80 % SZS status Theorem
% 0.63/0.80 % SZS output start Proof
% 0.63/0.80 tff(iext_type, type, (
% 0.63/0.80 iext: ( $i * $i * $i ) > $o)).
% 0.63/0.80 tff(tptp_fun_Y2_100_type, type, (
% 0.63/0.80 tptp_fun_Y2_100: ( $i * $i * $i ) > $i)).
% 0.63/0.80 tff(uri_ex_p_type, type, (
% 0.63/0.80 uri_ex_p: $i)).
% 0.63/0.80 tff(uri_ex_p1_type, type, (
% 0.63/0.80 uri_ex_p1: $i)).
% 0.63/0.80 tff(uri_ex_p2_type, type, (
% 0.63/0.80 uri_ex_p2: $i)).
% 0.63/0.80 tff(tptp_fun_Y0_102_type, type, (
% 0.63/0.80 tptp_fun_Y0_102: ( $i * $i * $i ) > $i)).
% 0.63/0.80 tff(uri_ex_y_type, type, (
% 0.63/0.80 uri_ex_y: $i)).
% 0.63/0.80 tff(uri_ex_x_type, type, (
% 0.63/0.80 uri_ex_x: $i)).
% 0.63/0.80 tff(icext_type, type, (
% 0.63/0.80 icext: ( $i * $i ) > $o)).
% 0.63/0.80 tff(tptp_fun_X3_140_type, type, (
% 0.63/0.80 tptp_fun_X3_140: $i)).
% 0.63/0.80 tff(ic_type, type, (
% 0.63/0.80 ic: $i > $o)).
% 0.63/0.80 tff(tptp_fun_X2_145_type, type, (
% 0.63/0.80 tptp_fun_X2_145: $i)).
% 0.63/0.80 tff(uri_owl_oneOf_type, type, (
% 0.63/0.80 uri_owl_oneOf: $i)).
% 0.63/0.80 tff(tptp_fun_X_8_type, type, (
% 0.63/0.80 tptp_fun_X_8: ( $i * $i ) > $i)).
% 0.63/0.80 tff(uri_rdf_nil_type, type, (
% 0.63/0.80 uri_rdf_nil: $i)).
% 0.63/0.80 tff(uri_rdf_rest_type, type, (
% 0.63/0.80 uri_rdf_rest: $i)).
% 0.63/0.80 tff(tptp_fun_X4_143_type, type, (
% 0.63/0.80 tptp_fun_X4_143: $i)).
% 0.63/0.80 tff(tptp_fun_X5_142_type, type, (
% 0.63/0.80 tptp_fun_X5_142: $i)).
% 0.63/0.80 tff(uri_rdf_first_type, type, (
% 0.63/0.80 uri_rdf_first: $i)).
% 0.63/0.80 tff(tptp_fun_X1_144_type, type, (
% 0.63/0.80 tptp_fun_X1_144: $i)).
% 0.63/0.80 tff(tptp_fun_X0_141_type, type, (
% 0.63/0.80 tptp_fun_X0_141: $i)).
% 0.63/0.80 tff(uri_rdfs_range_type, type, (
% 0.63/0.80 uri_rdfs_range: $i)).
% 0.63/0.80 tff(uri_ex_z_type, type, (
% 0.63/0.80 uri_ex_z: $i)).
% 0.63/0.80 tff(uri_rdfs_domain_type, type, (
% 0.63/0.80 uri_rdfs_domain: $i)).
% 0.63/0.80 tff(tptp_fun_Y1_101_type, type, (
% 0.63/0.80 tptp_fun_Y1_101: ( $i * $i * $i ) > $i)).
% 0.63/0.80 tff(ip_type, type, (
% 0.63/0.80 ip: $i > $o)).
% 0.63/0.80 tff(uri_owl_propertyChainAxiom_type, type, (
% 0.63/0.80 uri_owl_propertyChainAxiom: $i)).
% 0.63/0.80 tff(tptp_fun_Y_59_type, type, (
% 0.63/0.80 tptp_fun_Y_59: ( $i * $i ) > $i)).
% 0.63/0.80 tff(tptp_fun_X_60_type, type, (
% 0.63/0.80 tptp_fun_X_60: ( $i * $i ) > $i)).
% 0.63/0.80 tff(tptp_fun_X_58_type, type, (
% 0.63/0.80 tptp_fun_X_58: ( $i * $i ) > $i)).
% 0.63/0.80 tff(tptp_fun_Y_57_type, type, (
% 0.63/0.80 tptp_fun_Y_57: ( $i * $i ) > $i)).
% 0.63/0.80 tff(1,plain,
% 0.63/0.80 (?[X2: $i, X1: $i, X4: $i, X5: $i, X0: $i, X3: $i] : (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2) & iext(uri_rdf_first, X5, uri_ex_p1) & iext(uri_rdf_rest, X5, X4)) <=> ?[X2: $i, X1: $i, X4: $i, X5: $i, X0: $i, X3: $i] : (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2) & iext(uri_rdf_first, X5, uri_ex_p1) & iext(uri_rdf_rest, X5, X4))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2,plain,
% 0.63/0.80 (^[X2: $i, X1: $i, X4: $i, X5: $i, X0: $i, X3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x))), ((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil))), ((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil)))), (((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y))), (((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y)))), ((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil))), ((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil)))), (((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z))), (((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)))), ((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y))), ((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y)))), (((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3))), (((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3)))), ((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2))), ((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2)))), (((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil))), (((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil)))), ((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1))), ((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1)))), (((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) & iext(uri_owl_oneOf, X3, X2)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1)) & iext(uri_owl_oneOf, X3, X2)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1)) & iext(uri_owl_oneOf, X3, X2)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2))), (((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) & iext(uri_owl_oneOf, X3, X2)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2)))), ((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) & iext(uri_owl_oneOf, X3, X2)) & iext(uri_rdf_first, X5, uri_ex_p1)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2)) & iext(uri_rdf_first, X5, uri_ex_p1)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2)) & iext(uri_rdf_first, X5, uri_ex_p1)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2) & iext(uri_rdf_first, X5, uri_ex_p1))), ((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) & iext(uri_owl_oneOf, X3, X2)) & iext(uri_rdf_first, X5, uri_ex_p1)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2) & iext(uri_rdf_first, X5, uri_ex_p1)))), (((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) & iext(uri_owl_oneOf, X3, X2)) & iext(uri_rdf_first, X5, uri_ex_p1)) & iext(uri_rdf_rest, X5, X4)) <=> ((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2) & iext(uri_rdf_first, X5, uri_ex_p1)) & iext(uri_rdf_rest, X5, X4)))), rewrite(((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2) & iext(uri_rdf_first, X5, uri_ex_p1)) & iext(uri_rdf_rest, X5, X4)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2) & iext(uri_rdf_first, X5, uri_ex_p1) & iext(uri_rdf_rest, X5, X4))), (((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) & iext(uri_owl_oneOf, X3, X2)) & iext(uri_rdf_first, X5, uri_ex_p1)) & iext(uri_rdf_rest, X5, X4)) <=> (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2) & iext(uri_rdf_first, X5, uri_ex_p1) & iext(uri_rdf_rest, X5, X4))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(3,plain,
% 0.63/0.82 (?[X2: $i, X1: $i, X4: $i, X5: $i, X0: $i, X3: $i] : ((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) & iext(uri_owl_oneOf, X3, X2)) & iext(uri_rdf_first, X5, uri_ex_p1)) & iext(uri_rdf_rest, X5, X4)) <=> ?[X2: $i, X1: $i, X4: $i, X5: $i, X0: $i, X3: $i] : (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2) & iext(uri_rdf_first, X5, uri_ex_p1) & iext(uri_rdf_rest, X5, X4))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[2])).
% 0.63/0.82 tff(4,axiom,(?[X2: $i, X1: $i, X4: $i, X5: $i, X0: $i, X3: $i] : ((((((((((((((iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y)) & iext(uri_rdf_first, X1, uri_ex_x)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X2, uri_ex_y)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) & iext(uri_ex_p1, uri_ex_x, uri_ex_z)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_range, uri_ex_p2, X3)) & iext(uri_rdf_first, X4, uri_ex_p2)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_oneOf, X0, X1)) & iext(uri_owl_oneOf, X3, X2)) & iext(uri_rdf_first, X5, uri_ex_p1)) & iext(uri_rdf_rest, X5, X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','premise_rdfbased_sem_chain_ext')).
% 0.63/0.82 tff(5,plain,
% 0.63/0.82 (?[X2: $i, X1: $i, X4: $i, X5: $i, X0: $i, X3: $i] : (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2) & iext(uri_rdf_first, X5, uri_ex_p1) & iext(uri_rdf_rest, X5, X4))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.63/0.82 tff(6,plain,
% 0.63/0.82 (?[X2: $i, X1: $i, X4: $i, X5: $i, X0: $i, X3: $i] : (iext(uri_rdfs_domain, uri_ex_p1, X0) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1, uri_ex_x) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X2, uri_ex_y) & iext(uri_rdf_rest, X2, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3) & iext(uri_rdf_first, X4, uri_ex_p2) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_oneOf, X0, X1) & iext(uri_owl_oneOf, X3, X2) & iext(uri_rdf_first, X5, uri_ex_p1) & iext(uri_rdf_rest, X5, X4))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.63/0.82 tff(7,plain,(
% 0.63/0.82 iext(uri_rdfs_domain, uri_ex_p1, X0!141) & iext(uri_ex_p2, uri_ex_z, uri_ex_y) & iext(uri_rdf_first, X1!144, uri_ex_x) & iext(uri_rdf_rest, X1!144, uri_rdf_nil) & iext(uri_rdf_first, X2!145, uri_ex_y) & iext(uri_rdf_rest, X2!145, uri_rdf_nil) & iext(uri_ex_p1, uri_ex_x, uri_ex_z) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_range, uri_ex_p2, X3!140) & iext(uri_rdf_first, X4!143, uri_ex_p2) & iext(uri_rdf_rest, X4!143, uri_rdf_nil) & iext(uri_owl_oneOf, X0!141, X1!144) & iext(uri_owl_oneOf, X3!140, X2!145) & iext(uri_rdf_first, X5!142, uri_ex_p1) & iext(uri_rdf_rest, X5!142, X4!143)),
% 0.63/0.82 inference(skolemize,[status(sab)],[6])).
% 0.63/0.82 tff(8,plain,
% 0.63/0.82 (iext(uri_rdf_rest, X2!145, uri_rdf_nil)),
% 0.63/0.82 inference(and_elim,[status(thm)],[7])).
% 0.63/0.82 tff(9,plain,
% 0.63/0.82 (iext(uri_rdf_first, X2!145, uri_ex_y)),
% 0.63/0.82 inference(and_elim,[status(thm)],[7])).
% 0.63/0.82 tff(10,plain,
% 0.63/0.82 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(11,plain,
% 0.63/0.82 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[10])).
% 0.63/0.82 tff(12,plain,
% 0.63/0.82 (^[Z: $i, S1: $i, A1: $i] : refl(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(13,plain,
% 0.63/0.82 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[12])).
% 0.63/0.82 tff(14,plain,
% 0.63/0.82 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(15,plain,
% 0.63/0.82 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[14])).
% 0.63/0.82 tff(16,plain,
% 0.63/0.82 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[15, 13])).
% 0.63/0.82 tff(17,plain,
% 0.63/0.82 (^[Z: $i, S1: $i, A1: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) <=> ((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))), trans(monotonicity(rewrite((~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))) <=> (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))), rewrite((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> (((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))), rewrite((((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))) <=> (((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))))), rewrite((((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(18,plain,
% 0.63/0.82 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[17])).
% 0.63/0.82 tff(19,plain,
% 0.63/0.82 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(20,plain,
% 0.63/0.82 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[19])).
% 0.63/0.82 tff(21,plain,
% 0.63/0.82 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(22,plain,
% 0.63/0.82 (^[Z: $i, S1: $i, A1: $i] : trans(monotonicity(monotonicity(rewrite((ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))), ((iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), (((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), (((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(23,plain,
% 0.63/0.82 (![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[22])).
% 0.63/0.82 tff(24,axiom,(![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_enum_class_001')).
% 0.63/0.82 tff(25,plain,
% 0.63/0.82 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.63/0.82 tff(26,plain,
% 0.63/0.82 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.63/0.82 tff(27,plain,(
% 0.63/0.82 ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.63/0.82 inference(skolemize,[status(sab)],[26])).
% 0.63/0.82 tff(28,plain,
% 0.63/0.82 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.63/0.83 tff(29,plain,
% 0.63/0.83 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.63/0.83 tff(30,plain,
% 0.63/0.83 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.63/0.83 tff(31,plain,
% 0.63/0.83 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[30, 11])).
% 0.63/0.83 tff(32,plain,
% 0.63/0.83 (((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, X2!145, uri_ex_y)) | (~iext(uri_rdf_rest, X2!145, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X3!140, X2!145) | (~ic(X3!140)) | (~(icext(X3!140, tptp_fun_X_8(uri_ex_y, X3!140)) <=> (tptp_fun_X_8(uri_ex_y, X3!140) = uri_ex_y))))) | (~((~iext(uri_owl_oneOf, X3!140, X2!145)) | (~((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, X2!145, uri_ex_y)) | (~iext(uri_rdf_rest, X2!145, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X3!140, X2!145) | (~ic(X3!140)) | (~(icext(X3!140, tptp_fun_X_8(uri_ex_y, X3!140)) <=> (tptp_fun_X_8(uri_ex_y, X3!140) = uri_ex_y))))) | (~((~iext(uri_owl_oneOf, X3!140, X2!145)) | (~((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y))))))))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(33,plain,
% 0.63/0.83 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, X2!145, uri_ex_y)) | (~iext(uri_rdf_rest, X2!145, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X3!140, X2!145) | (~ic(X3!140)) | (~(icext(X3!140, tptp_fun_X_8(uri_ex_y, X3!140)) <=> (tptp_fun_X_8(uri_ex_y, X3!140) = uri_ex_y))))) | (~((~iext(uri_owl_oneOf, X3!140, X2!145)) | (~((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y))))))))))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(34,plain,
% 0.63/0.83 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, X2!145, uri_ex_y)) | (~iext(uri_rdf_rest, X2!145, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X3!140, X2!145) | (~ic(X3!140)) | (~(icext(X3!140, tptp_fun_X_8(uri_ex_y, X3!140)) <=> (tptp_fun_X_8(uri_ex_y, X3!140) = uri_ex_y))))) | (~((~iext(uri_owl_oneOf, X3!140, X2!145)) | (~((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y)))))))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.63/0.83 tff(35,plain,
% 0.63/0.83 (~((~(iext(uri_owl_oneOf, X3!140, X2!145) | (~ic(X3!140)) | (~(icext(X3!140, tptp_fun_X_8(uri_ex_y, X3!140)) <=> (tptp_fun_X_8(uri_ex_y, X3!140) = uri_ex_y))))) | (~((~iext(uri_owl_oneOf, X3!140, X2!145)) | (~((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y))))))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[34, 31, 9, 8])).
% 0.63/0.83 tff(36,plain,
% 0.63/0.83 (((~(iext(uri_owl_oneOf, X3!140, X2!145) | (~ic(X3!140)) | (~(icext(X3!140, tptp_fun_X_8(uri_ex_y, X3!140)) <=> (tptp_fun_X_8(uri_ex_y, X3!140) = uri_ex_y))))) | (~((~iext(uri_owl_oneOf, X3!140, X2!145)) | (~((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y)))))))) | ((~iext(uri_owl_oneOf, X3!140, X2!145)) | (~((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y))))))),
% 0.63/0.83 inference(tautology,[status(thm)],[])).
% 0.63/0.83 tff(37,plain,
% 0.63/0.83 ((~iext(uri_owl_oneOf, X3!140, X2!145)) | (~((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y)))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.63/0.83 tff(38,plain,
% 0.63/0.83 (iext(uri_owl_oneOf, X3!140, X2!145)),
% 0.63/0.83 inference(and_elim,[status(thm)],[7])).
% 0.63/0.83 tff(39,plain,
% 0.63/0.83 ((~((~iext(uri_owl_oneOf, X3!140, X2!145)) | (~((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y))))))) | (~iext(uri_owl_oneOf, X3!140, X2!145)) | (~((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y)))))),
% 0.63/0.83 inference(tautology,[status(thm)],[])).
% 0.63/0.83 tff(40,plain,
% 0.63/0.83 ((~((~iext(uri_owl_oneOf, X3!140, X2!145)) | (~((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y))))))) | (~((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y)))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.63/0.83 tff(41,plain,
% 0.63/0.83 (~((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.63/0.83 tff(42,plain,
% 0.63/0.83 (((~ic(X3!140)) | (~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y)))) | ![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y))),
% 0.63/0.83 inference(tautology,[status(thm)],[])).
% 0.63/0.83 tff(43,plain,
% 0.63/0.83 (![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.63/0.83 tff(44,plain,
% 0.63/0.83 ((~![X: $i] : (icext(X3!140, X) <=> (X = uri_ex_y))) | (icext(X3!140, tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)) <=> (tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_y))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(45,plain,
% 0.63/0.83 (icext(X3!140, tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)) <=> (tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_y)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.63/0.83 tff(46,plain,
% 0.63/0.83 (iext(uri_rdf_rest, X5!142, X4!143)),
% 0.63/0.83 inference(and_elim,[status(thm)],[7])).
% 0.63/0.83 tff(47,plain,
% 0.63/0.83 (iext(uri_rdf_first, X5!142, uri_ex_p1)),
% 0.63/0.83 inference(and_elim,[status(thm)],[7])).
% 0.63/0.83 tff(48,plain,
% 0.63/0.83 (iext(uri_rdf_rest, X4!143, uri_rdf_nil)),
% 0.63/0.83 inference(and_elim,[status(thm)],[7])).
% 0.63/0.83 tff(49,plain,
% 0.63/0.83 (iext(uri_rdf_first, X4!143, uri_ex_p2)),
% 0.63/0.83 inference(and_elim,[status(thm)],[7])).
% 0.63/0.83 tff(50,plain,
% 0.63/0.83 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))))))), (((~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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))))))))), 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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))))))) <=> ((~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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))), (((~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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(51,plain,
% 0.63/0.83 (![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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[50])).
% 0.63/0.83 tff(52,plain,
% 0.63/0.83 (^[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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(53,plain,
% 0.63/0.83 (![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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[52])).
% 0.63/0.83 tff(54,plain,
% 0.63/0.83 (^[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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(55,plain,
% 0.63/0.83 (![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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[54])).
% 0.63/0.83 tff(56,plain,
% 0.63/0.83 (![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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[55, 53])).
% 0.63/0.83 tff(57,plain,
% 0.63/0.83 (^[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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))), trans(monotonicity(rewrite((~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) <=> (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))) <=> (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))), rewrite((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(58,plain,
% 0.63/0.83 (![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(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[57])).
% 0.63/0.83 tff(59,plain,
% 0.63/0.83 (^[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_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(60,plain,
% 0.63/0.83 (![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_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(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(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[59])).
% 0.63/0.83 tff(61,plain,
% 0.63/0.83 (![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)))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(62,plain,
% 0.63/0.83 (^[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)))))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(63,plain,
% 0.63/0.83 (![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)))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[62])).
% 0.63/0.83 tff(64,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/Axioms/SWB001+0.ax','owl_chain_002')).
% 0.63/0.83 tff(65,plain,
% 0.63/0.83 (![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)))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.63/0.83 tff(66,plain,
% 0.63/0.83 (![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)))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.63/0.84 tff(67,plain,(
% 0.63/0.84 ![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_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))),
% 0.63/0.84 inference(skolemize,[status(sab)],[66])).
% 0.63/0.84 tff(68,plain,
% 0.63/0.84 (![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(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.63/0.84 tff(69,plain,
% 0.63/0.84 (![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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.63/0.84 tff(70,plain,
% 0.63/0.84 (![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(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[69, 56])).
% 0.63/0.84 tff(71,plain,
% 0.63/0.84 (![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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[70, 51])).
% 0.63/0.84 tff(72,plain,
% 0.63/0.84 (((~![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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y2))))))))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(73,plain,
% 0.63/0.84 (((~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y2)))))))))) <=> ((~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y2))))))))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(74,plain,
% 0.63/0.84 ((~((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~(iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_p, Y0, Y2) | (~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)))))))))) <=> (~((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y2)))))))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(75,plain,
% 0.63/0.84 (((~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~(iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_p, Y0, Y2) | (~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y2))))))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[74])).
% 0.63/0.84 tff(76,plain,
% 0.63/0.84 (((~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~(iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_p, Y0, Y2) | (~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y2))))))))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[75, 73])).
% 0.63/0.84 tff(77,plain,
% 0.63/0.84 (((~![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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~(iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_p, Y0, Y2) | (~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)))))))))))) <=> ((~![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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y2)))))))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[76])).
% 0.63/0.84 tff(78,plain,
% 0.63/0.84 (((~![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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~(iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_p, Y0, Y2) | (~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)))))))))))) <=> ((~![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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y2))))))))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[77, 72])).
% 0.63/0.84 tff(79,plain,
% 0.63/0.84 ((~![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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~(iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p2)) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_p, Y0, Y2) | (~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)))))))))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(80,plain,
% 0.63/0.84 ((~![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(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y2)))))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.63/0.84 tff(81,plain,
% 0.63/0.84 (~((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y2))))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[80, 71, 49, 48, 47, 46])).
% 0.63/0.84 tff(82,plain,
% 0.63/0.84 (((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_p2, Y1, Y2)) | (~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y2)))))))) | ((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))),
% 0.63/0.84 inference(tautology,[status(thm)],[])).
% 0.63/0.84 tff(83,plain,
% 0.63/0.84 ((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.63/0.84 tff(84,plain,
% 0.63/0.84 (^[X0: $i, X1: $i] : refl(((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1))) <=> ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(85,plain,
% 0.63/0.84 (![X0: $i, X1: $i] : ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1))) <=> ![X0: $i, X1: $i] : ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[84])).
% 0.63/0.84 tff(86,plain,
% 0.63/0.84 (^[X0: $i, X1: $i] : trans(monotonicity(rewrite((iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1)) <=> (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1))))), ((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1))) <=> (~(~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1))))))), rewrite((~(~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1))))) <=> ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))), ((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1))) <=> ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(87,plain,
% 0.63/0.85 (![X0: $i, X1: $i] : (~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1))) <=> ![X0: $i, X1: $i] : ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[86])).
% 0.63/0.85 tff(88,plain,
% 0.63/0.85 ((~?[X0: $i, X1: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1))) <=> (~?[X0: $i, X1: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(89,plain,
% 0.63/0.85 ((~?[X0: $i, X1: $i] : ((((iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X0, uri_ex_p1)) & iext(uri_rdf_rest, X0, X1))) <=> (~?[X0: $i, X1: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(90,axiom,(~?[X0: $i, X1: $i] : ((((iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X0, uri_ex_p1)) & iext(uri_rdf_rest, X0, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conclusion_rdfbased_sem_chain_ext')).
% 0.63/0.85 tff(91,plain,
% 0.63/0.85 (~?[X0: $i, X1: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.63/0.85 tff(92,plain,
% 0.63/0.85 (~?[X0: $i, X1: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[91, 88])).
% 0.63/0.85 tff(93,plain,
% 0.63/0.85 (~?[X0: $i, X1: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.63/0.85 tff(94,plain,
% 0.63/0.85 (~?[X0: $i, X1: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[93, 88])).
% 0.63/0.85 tff(95,plain,
% 0.63/0.85 (^[X0: $i, X1: $i] : refl($oeq((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1))), (~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1)))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(96,plain,(
% 0.63/0.85 ![X0: $i, X1: $i] : (~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X1, uri_ex_p2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, X1)))),
% 0.63/0.85 inference(nnf-neg,[status(sab)],[94, 95])).
% 0.63/0.85 tff(97,plain,
% 0.63/0.85 (![X0: $i, X1: $i] : ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[96, 87])).
% 0.63/0.85 tff(98,plain,
% 0.63/0.85 (![X0: $i, X1: $i] : ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[97, 85])).
% 0.63/0.85 tff(99,plain,
% 0.63/0.85 (((~![X0: $i, X1: $i] : ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))) | ((~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)))) <=> ((~![X0: $i, X1: $i] : ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(100,plain,
% 0.63/0.85 (((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143))) <=> ((~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(101,plain,
% 0.63/0.85 (((~![X0: $i, X1: $i] : ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))) | ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)))) <=> ((~![X0: $i, X1: $i] : ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))) | ((~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[100])).
% 0.63/0.85 tff(102,plain,
% 0.63/0.85 (((~![X0: $i, X1: $i] : ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))) | ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)))) <=> ((~![X0: $i, X1: $i] : ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[101, 99])).
% 0.63/0.85 tff(103,plain,
% 0.63/0.85 ((~![X0: $i, X1: $i] : ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))) | ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(104,plain,
% 0.63/0.85 ((~![X0: $i, X1: $i] : ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0)) | (~iext(uri_rdf_first, X1, uri_ex_p2)) | (~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_rdf_first, X0, uri_ex_p1)) | (~iext(uri_rdf_rest, X0, X1)))) | (~iext(uri_rdf_first, X4!143, uri_ex_p2)) | (~iext(uri_rdf_rest, X4!143, uri_rdf_nil)) | (~iext(uri_rdf_first, X5!142, uri_ex_p1)) | (~iext(uri_rdf_rest, X5!142, X4!143)) | (~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.63/0.85 tff(105,plain,
% 0.63/0.85 (~iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[104, 98, 49, 48, 47, 46])).
% 0.63/0.85 tff(106,plain,
% 0.63/0.85 (iext(uri_ex_p, uri_ex_x, uri_ex_y)),
% 0.63/0.85 inference(and_elim,[status(thm)],[7])).
% 0.63/0.85 tff(107,plain,
% 0.63/0.85 (^[S: $i, P: $i, O: $i] : refl((ip(P) | (~iext(P, S, O))) <=> (ip(P) | (~iext(P, S, O))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(108,plain,
% 0.63/0.85 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O))) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[107])).
% 0.63/0.85 tff(109,plain,
% 0.63/0.85 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O))) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(110,plain,
% 0.63/0.85 (^[S: $i, P: $i, O: $i] : rewrite((iext(P, S, O) => ip(P)) <=> (ip(P) | (~iext(P, S, O))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(111,plain,
% 0.63/0.85 (![S: $i, P: $i, O: $i] : (iext(P, S, O) => ip(P)) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[110])).
% 0.63/0.85 tff(112,axiom,(![S: $i, P: $i, O: $i] : (iext(P, S, O) => ip(P))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','simple_iext_property')).
% 0.63/0.85 tff(113,plain,
% 0.63/0.85 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.63/0.85 tff(114,plain,
% 0.63/0.85 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.63/0.85 tff(115,plain,(
% 0.63/0.85 ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.63/0.85 inference(skolemize,[status(sab)],[114])).
% 0.63/0.85 tff(116,plain,
% 0.63/0.85 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.63/0.85 tff(117,plain,
% 0.63/0.85 (((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | (ip(uri_ex_p) | (~iext(uri_ex_p, uri_ex_x, uri_ex_y)))) <=> ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | ip(uri_ex_p) | (~iext(uri_ex_p, uri_ex_x, uri_ex_y)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(118,plain,
% 0.63/0.85 ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | (ip(uri_ex_p) | (~iext(uri_ex_p, uri_ex_x, uri_ex_y)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(119,plain,
% 0.63/0.85 ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | ip(uri_ex_p) | (~iext(uri_ex_p, uri_ex_x, uri_ex_y))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.63/0.85 tff(120,plain,
% 0.63/0.85 (ip(uri_ex_p)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[119, 116, 106])).
% 0.63/0.85 tff(121,plain,
% 0.63/0.85 (iext(uri_ex_p2, uri_ex_z, uri_ex_y)),
% 0.63/0.85 inference(and_elim,[status(thm)],[7])).
% 0.63/0.85 tff(122,plain,
% 0.63/0.85 (((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | (ip(uri_ex_p2) | (~iext(uri_ex_p2, uri_ex_z, uri_ex_y)))) <=> ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | ip(uri_ex_p2) | (~iext(uri_ex_p2, uri_ex_z, uri_ex_y)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(123,plain,
% 0.63/0.85 ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | (ip(uri_ex_p2) | (~iext(uri_ex_p2, uri_ex_z, uri_ex_y)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(124,plain,
% 0.63/0.85 ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | ip(uri_ex_p2) | (~iext(uri_ex_p2, uri_ex_z, uri_ex_y))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.63/0.85 tff(125,plain,
% 0.63/0.85 (ip(uri_ex_p2)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[124, 116, 121])).
% 0.63/0.85 tff(126,plain,
% 0.63/0.85 (iext(uri_ex_p1, uri_ex_x, uri_ex_z)),
% 0.63/0.85 inference(and_elim,[status(thm)],[7])).
% 0.63/0.85 tff(127,plain,
% 0.63/0.85 (((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | (ip(uri_ex_p1) | (~iext(uri_ex_p1, uri_ex_x, uri_ex_z)))) <=> ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | ip(uri_ex_p1) | (~iext(uri_ex_p1, uri_ex_x, uri_ex_z)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(128,plain,
% 0.63/0.85 ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | (ip(uri_ex_p1) | (~iext(uri_ex_p1, uri_ex_x, uri_ex_z)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(129,plain,
% 0.63/0.85 ((~![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))) | ip(uri_ex_p1) | (~iext(uri_ex_p1, uri_ex_x, uri_ex_z))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.63/0.85 tff(130,plain,
% 0.63/0.85 (ip(uri_ex_p1)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[129, 116, 126])).
% 0.63/0.85 tff(131,plain,
% 0.63/0.85 ((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(132,plain,
% 0.63/0.85 ((~((~ip(uri_ex_p1)) | (~ip(uri_ex_p2)) | iext(uri_owl_propertyChainAxiom, uri_ex_p, X5!142) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[131, 130, 125, 120, 105])).
% 0.63/0.85 tff(133,plain,
% 0.63/0.85 (~((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[132, 83])).
% 0.63/0.85 tff(134,plain,
% 0.63/0.85 (((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(135,plain,
% 0.63/0.85 (iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.63/0.85 tff(136,plain,
% 0.63/0.85 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(137,plain,
% 0.63/0.85 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> ![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[136])).
% 0.63/0.85 tff(138,plain,
% 0.63/0.85 (^[P: $i, C: $i] : refl((~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(139,plain,
% 0.63/0.85 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[138])).
% 0.63/0.85 tff(140,plain,
% 0.63/0.85 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(141,plain,
% 0.63/0.85 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[140])).
% 0.63/0.85 tff(142,plain,
% 0.63/0.85 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 0.63/0.85 inference(transitivity,[status(thm)],[141, 139])).
% 0.63/0.85 tff(143,plain,
% 0.63/0.85 (^[P: $i, C: $i] : trans(monotonicity(rewrite(((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) <=> ((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))), rewrite((iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))) <=> (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))), ((((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) <=> (((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))), rewrite((((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) <=> (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))), ((((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) <=> (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(144,plain,
% 0.63/0.85 (![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[143])).
% 0.63/0.85 tff(145,plain,
% 0.63/0.85 (^[P: $i, C: $i] : rewrite((((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | ((~ip(P)) | (~ip(C)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))) <=> (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(146,plain,
% 0.63/0.85 (![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | ((~ip(P)) | (~ip(C)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))) <=> ![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[145])).
% 0.63/0.85 tff(147,plain,
% 0.63/0.85 (![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(148,plain,
% 0.63/0.85 (^[P: $i, C: $i] : rewrite((iext(uri_rdfs_range, P, C) <=> ((ip(P) & ip(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, Y)))) <=> (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(149,plain,
% 0.63/0.85 (![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> ((ip(P) & ip(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, Y)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[148])).
% 0.63/0.85 tff(150,axiom,(![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> ((ip(P) & ip(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_rdfsext_range')).
% 0.63/0.85 tff(151,plain,
% 0.63/0.85 (![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.63/0.85 tff(152,plain,
% 0.63/0.85 (![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.63/0.85 tff(153,plain,(
% 0.63/0.85 ![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | ((~ip(P)) | (~ip(C)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))),
% 0.63/0.85 inference(skolemize,[status(sab)],[152])).
% 0.63/0.85 tff(154,plain,
% 0.63/0.85 (![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.63/0.85 tff(155,plain,
% 0.63/0.85 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[154, 144])).
% 0.63/0.85 tff(156,plain,
% 0.63/0.85 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[155, 142])).
% 0.63/0.85 tff(157,plain,
% 0.63/0.85 (![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[156, 137])).
% 0.63/0.85 tff(158,plain,
% 0.63/0.85 (((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_ex_p2, X3!140) | (~ip(uri_ex_p2)) | (~ip(X3!140)) | (~((~iext(uri_ex_p2, tptp_fun_X_60(X3!140, uri_ex_p2), tptp_fun_Y_59(X3!140, uri_ex_p2))) | icext(X3!140, tptp_fun_Y_59(X3!140, uri_ex_p2)))))) | (~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y)))))))))) <=> ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_ex_p2, X3!140) | (~ip(uri_ex_p2)) | (~ip(X3!140)) | (~((~iext(uri_ex_p2, tptp_fun_X_60(X3!140, uri_ex_p2), tptp_fun_Y_59(X3!140, uri_ex_p2))) | icext(X3!140, tptp_fun_Y_59(X3!140, uri_ex_p2)))))) | (~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))))))))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(159,plain,
% 0.63/0.85 ((~((~(iext(uri_rdfs_range, uri_ex_p2, X3!140) | (~ip(X3!140)) | (~ip(uri_ex_p2)) | (~((~iext(uri_ex_p2, tptp_fun_X_60(X3!140, uri_ex_p2), tptp_fun_Y_59(X3!140, uri_ex_p2))) | icext(X3!140, tptp_fun_Y_59(X3!140, uri_ex_p2)))))) | (~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))))))))) <=> (~((~(iext(uri_rdfs_range, uri_ex_p2, X3!140) | (~ip(uri_ex_p2)) | (~ip(X3!140)) | (~((~iext(uri_ex_p2, tptp_fun_X_60(X3!140, uri_ex_p2), tptp_fun_Y_59(X3!140, uri_ex_p2))) | icext(X3!140, tptp_fun_Y_59(X3!140, uri_ex_p2)))))) | (~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y)))))))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(160,plain,
% 0.63/0.85 (((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_ex_p2, X3!140) | (~ip(X3!140)) | (~ip(uri_ex_p2)) | (~((~iext(uri_ex_p2, tptp_fun_X_60(X3!140, uri_ex_p2), tptp_fun_Y_59(X3!140, uri_ex_p2))) | icext(X3!140, tptp_fun_Y_59(X3!140, uri_ex_p2)))))) | (~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y)))))))))) <=> ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_ex_p2, X3!140) | (~ip(uri_ex_p2)) | (~ip(X3!140)) | (~((~iext(uri_ex_p2, tptp_fun_X_60(X3!140, uri_ex_p2), tptp_fun_Y_59(X3!140, uri_ex_p2))) | icext(X3!140, tptp_fun_Y_59(X3!140, uri_ex_p2)))))) | (~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))))))))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[159])).
% 0.63/0.85 tff(161,plain,
% 0.63/0.85 (((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_ex_p2, X3!140) | (~ip(X3!140)) | (~ip(uri_ex_p2)) | (~((~iext(uri_ex_p2, tptp_fun_X_60(X3!140, uri_ex_p2), tptp_fun_Y_59(X3!140, uri_ex_p2))) | icext(X3!140, tptp_fun_Y_59(X3!140, uri_ex_p2)))))) | (~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y)))))))))) <=> ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_ex_p2, X3!140) | (~ip(uri_ex_p2)) | (~ip(X3!140)) | (~((~iext(uri_ex_p2, tptp_fun_X_60(X3!140, uri_ex_p2), tptp_fun_Y_59(X3!140, uri_ex_p2))) | icext(X3!140, tptp_fun_Y_59(X3!140, uri_ex_p2)))))) | (~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))))))))))),
% 0.63/0.86 inference(transitivity,[status(thm)],[160, 158])).
% 0.63/0.86 tff(162,plain,
% 0.63/0.86 ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_ex_p2, X3!140) | (~ip(X3!140)) | (~ip(uri_ex_p2)) | (~((~iext(uri_ex_p2, tptp_fun_X_60(X3!140, uri_ex_p2), tptp_fun_Y_59(X3!140, uri_ex_p2))) | icext(X3!140, tptp_fun_Y_59(X3!140, uri_ex_p2)))))) | (~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y)))))))))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(163,plain,
% 0.63/0.86 ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_ex_p2, X3!140) | (~ip(uri_ex_p2)) | (~ip(X3!140)) | (~((~iext(uri_ex_p2, tptp_fun_X_60(X3!140, uri_ex_p2), tptp_fun_Y_59(X3!140, uri_ex_p2))) | icext(X3!140, tptp_fun_Y_59(X3!140, uri_ex_p2)))))) | (~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y)))))))))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.63/0.86 tff(164,plain,
% 0.63/0.86 (~((~(iext(uri_rdfs_range, uri_ex_p2, X3!140) | (~ip(uri_ex_p2)) | (~ip(X3!140)) | (~((~iext(uri_ex_p2, tptp_fun_X_60(X3!140, uri_ex_p2), tptp_fun_Y_59(X3!140, uri_ex_p2))) | icext(X3!140, tptp_fun_Y_59(X3!140, uri_ex_p2)))))) | (~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))))))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[163, 157])).
% 0.63/0.86 tff(165,plain,
% 0.63/0.86 (((~(iext(uri_rdfs_range, uri_ex_p2, X3!140) | (~ip(uri_ex_p2)) | (~ip(X3!140)) | (~((~iext(uri_ex_p2, tptp_fun_X_60(X3!140, uri_ex_p2), tptp_fun_Y_59(X3!140, uri_ex_p2))) | icext(X3!140, tptp_fun_Y_59(X3!140, uri_ex_p2)))))) | (~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y)))))))) | ((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))))))),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(166,plain,
% 0.63/0.86 ((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y)))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.63/0.86 tff(167,plain,
% 0.63/0.86 (iext(uri_rdfs_range, uri_ex_p2, X3!140)),
% 0.63/0.86 inference(and_elim,[status(thm)],[7])).
% 0.63/0.86 tff(168,plain,
% 0.63/0.86 ((~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))))))) | (~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y)))))),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(169,plain,
% 0.63/0.86 ((~((~iext(uri_rdfs_range, uri_ex_p2, X3!140)) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))))))) | (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y)))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.63/0.86 tff(170,plain,
% 0.63/0.86 (~((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[169, 166])).
% 0.63/0.86 tff(171,plain,
% 0.63/0.86 (((~ip(X3!140)) | (~ip(uri_ex_p2)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y)))) | ![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(172,plain,
% 0.63/0.86 (![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.63/0.86 tff(173,plain,
% 0.63/0.86 (((~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))) | ((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | icext(X3!140, tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))) | (~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | icext(X3!140, tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(174,plain,
% 0.63/0.86 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))) | ((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | icext(X3!140, tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(175,plain,
% 0.63/0.86 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p2, X, Y)) | icext(X3!140, Y))) | (~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | icext(X3!140, tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.63/0.86 tff(176,plain,
% 0.63/0.86 (icext(X3!140, tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[175, 172, 135])).
% 0.63/0.86 tff(177,plain,
% 0.63/0.86 ((~(icext(X3!140, tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)) <=> (tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_y))) | (~icext(X3!140, tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_y)),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(178,plain,
% 0.63/0.86 ((~(icext(X3!140, tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)) <=> (tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_y))) | (tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_y)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.63/0.86 tff(179,plain,
% 0.63/0.86 (tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_y),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[178, 45])).
% 0.63/0.86 tff(180,plain,
% 0.63/0.86 (iext(uri_rdf_rest, X1!144, uri_rdf_nil)),
% 0.63/0.86 inference(and_elim,[status(thm)],[7])).
% 0.63/0.86 tff(181,plain,
% 0.63/0.86 (iext(uri_rdf_first, X1!144, uri_ex_x)),
% 0.63/0.86 inference(and_elim,[status(thm)],[7])).
% 0.63/0.86 tff(182,plain,
% 0.63/0.86 (((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, X1!144, uri_ex_x)) | (~iext(uri_rdf_rest, X1!144, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X0!141, X1!144) | (~ic(X0!141)) | (~(icext(X0!141, tptp_fun_X_8(uri_ex_x, X0!141)) <=> (tptp_fun_X_8(uri_ex_x, X0!141) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, X0!141, X1!144)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, X1!144, uri_ex_x)) | (~iext(uri_rdf_rest, X1!144, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X0!141, X1!144) | (~ic(X0!141)) | (~(icext(X0!141, tptp_fun_X_8(uri_ex_x, X0!141)) <=> (tptp_fun_X_8(uri_ex_x, X0!141) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, X0!141, X1!144)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x))))))))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(183,plain,
% 0.63/0.86 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, X1!144, uri_ex_x)) | (~iext(uri_rdf_rest, X1!144, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X0!141, X1!144) | (~ic(X0!141)) | (~(icext(X0!141, tptp_fun_X_8(uri_ex_x, X0!141)) <=> (tptp_fun_X_8(uri_ex_x, X0!141) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, X0!141, X1!144)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x))))))))))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(184,plain,
% 0.63/0.86 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, X1!144, uri_ex_x)) | (~iext(uri_rdf_rest, X1!144, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X0!141, X1!144) | (~ic(X0!141)) | (~(icext(X0!141, tptp_fun_X_8(uri_ex_x, X0!141)) <=> (tptp_fun_X_8(uri_ex_x, X0!141) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, X0!141, X1!144)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x)))))))))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.63/0.86 tff(185,plain,
% 0.63/0.86 (~((~(iext(uri_owl_oneOf, X0!141, X1!144) | (~ic(X0!141)) | (~(icext(X0!141, tptp_fun_X_8(uri_ex_x, X0!141)) <=> (tptp_fun_X_8(uri_ex_x, X0!141) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, X0!141, X1!144)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x))))))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[184, 31, 181, 180])).
% 0.63/0.86 tff(186,plain,
% 0.63/0.86 (((~(iext(uri_owl_oneOf, X0!141, X1!144) | (~ic(X0!141)) | (~(icext(X0!141, tptp_fun_X_8(uri_ex_x, X0!141)) <=> (tptp_fun_X_8(uri_ex_x, X0!141) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, X0!141, X1!144)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x)))))))) | ((~iext(uri_owl_oneOf, X0!141, X1!144)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x))))))),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(187,plain,
% 0.63/0.86 ((~iext(uri_owl_oneOf, X0!141, X1!144)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x)))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.63/0.86 tff(188,plain,
% 0.63/0.86 (iext(uri_owl_oneOf, X0!141, X1!144)),
% 0.63/0.86 inference(and_elim,[status(thm)],[7])).
% 0.63/0.86 tff(189,plain,
% 0.63/0.86 ((~((~iext(uri_owl_oneOf, X0!141, X1!144)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x))))))) | (~iext(uri_owl_oneOf, X0!141, X1!144)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x)))))),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(190,plain,
% 0.63/0.86 ((~((~iext(uri_owl_oneOf, X0!141, X1!144)) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x))))))) | (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x)))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.63/0.86 tff(191,plain,
% 0.63/0.86 (~((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[190, 187])).
% 0.63/0.86 tff(192,plain,
% 0.63/0.86 (((~ic(X0!141)) | (~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x)))) | ![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x))),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(193,plain,
% 0.63/0.86 (![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.63/0.86 tff(194,plain,
% 0.63/0.86 ((~![X: $i] : (icext(X0!141, X) <=> (X = uri_ex_x))) | (icext(X0!141, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p)) <=> (tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_x))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(195,plain,
% 0.63/0.86 (icext(X0!141, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p)) <=> (tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_x)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.63/0.86 tff(196,plain,
% 0.63/0.86 (((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(197,plain,
% 0.63/0.86 (iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[196, 133])).
% 0.63/0.86 tff(198,plain,
% 0.63/0.86 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))))))),
% 0.63/0.86 inference(bind,[status(th)],[])).
% 0.63/0.86 tff(199,plain,
% 0.63/0.86 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))),
% 0.63/0.86 inference(quant_intro,[status(thm)],[198])).
% 0.63/0.86 tff(200,plain,
% 0.63/0.86 (^[P: $i, C: $i] : refl((~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))))),
% 0.63/0.86 inference(bind,[status(th)],[])).
% 0.63/0.86 tff(201,plain,
% 0.63/0.86 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 0.63/0.86 inference(quant_intro,[status(thm)],[200])).
% 0.63/0.86 tff(202,plain,
% 0.63/0.86 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))))),
% 0.63/0.86 inference(bind,[status(th)],[])).
% 0.63/0.86 tff(203,plain,
% 0.63/0.86 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 0.63/0.86 inference(quant_intro,[status(thm)],[202])).
% 0.63/0.86 tff(204,plain,
% 0.63/0.86 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 0.63/0.86 inference(transitivity,[status(thm)],[203, 201])).
% 0.63/0.86 tff(205,plain,
% 0.63/0.86 (^[P: $i, C: $i] : trans(monotonicity(rewrite(((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) <=> ((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))), rewrite((iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))) <=> (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))), ((((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> (((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))), rewrite((((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))), ((((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))))),
% 0.63/0.86 inference(bind,[status(th)],[])).
% 0.63/0.86 tff(206,plain,
% 0.63/0.86 (![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 0.63/0.86 inference(quant_intro,[status(thm)],[205])).
% 0.63/0.86 tff(207,plain,
% 0.63/0.86 (^[P: $i, C: $i] : rewrite((((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | ((~ip(P)) | (~ic(C)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))) <=> (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))),
% 0.63/0.86 inference(bind,[status(th)],[])).
% 0.63/0.86 tff(208,plain,
% 0.63/0.86 (![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | ((~ip(P)) | (~ic(C)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))) <=> ![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))),
% 0.63/0.86 inference(quant_intro,[status(thm)],[207])).
% 0.63/0.86 tff(209,plain,
% 0.63/0.86 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(210,plain,
% 0.63/0.86 (^[P: $i, C: $i] : rewrite((iext(uri_rdfs_domain, P, C) <=> ((ip(P) & ic(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, X)))) <=> (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))),
% 0.63/0.86 inference(bind,[status(th)],[])).
% 0.63/0.86 tff(211,plain,
% 0.63/0.86 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> ((ip(P) & ic(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, X)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 0.63/0.86 inference(quant_intro,[status(thm)],[210])).
% 0.63/0.86 tff(212,axiom,(![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> ((ip(P) & ic(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_rdfsext_domain')).
% 0.63/0.86 tff(213,plain,
% 0.63/0.86 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.63/0.86 tff(214,plain,
% 0.63/0.86 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.63/0.86 tff(215,plain,(
% 0.63/0.86 ![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | ((~ip(P)) | (~ic(C)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))),
% 0.63/0.86 inference(skolemize,[status(sab)],[214])).
% 0.63/0.86 tff(216,plain,
% 0.63/0.86 (![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.63/0.86 tff(217,plain,
% 0.63/0.86 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[216, 206])).
% 0.70/0.86 tff(218,plain,
% 0.70/0.86 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[217, 204])).
% 0.70/0.86 tff(219,plain,
% 0.70/0.86 (![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[218, 199])).
% 0.70/0.86 tff(220,plain,
% 0.70/0.86 (((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!141) | (~ip(uri_ex_p1)) | (~ic(X0!141)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!141, uri_ex_p1), tptp_fun_Y_57(X0!141, uri_ex_p1))) | icext(X0!141, tptp_fun_X_58(X0!141, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X)))))))))) <=> ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!141) | (~ip(uri_ex_p1)) | (~ic(X0!141)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!141, uri_ex_p1), tptp_fun_Y_57(X0!141, uri_ex_p1))) | icext(X0!141, tptp_fun_X_58(X0!141, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))))))))))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(221,plain,
% 0.70/0.86 ((~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!141) | (~ic(X0!141)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!141, uri_ex_p1), tptp_fun_Y_57(X0!141, uri_ex_p1))) | icext(X0!141, tptp_fun_X_58(X0!141, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))))))))) <=> (~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!141) | (~ip(uri_ex_p1)) | (~ic(X0!141)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!141, uri_ex_p1), tptp_fun_Y_57(X0!141, uri_ex_p1))) | icext(X0!141, tptp_fun_X_58(X0!141, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X)))))))))),
% 0.70/0.86 inference(rewrite,[status(thm)],[])).
% 0.70/0.86 tff(222,plain,
% 0.70/0.86 (((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!141) | (~ic(X0!141)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!141, uri_ex_p1), tptp_fun_Y_57(X0!141, uri_ex_p1))) | icext(X0!141, tptp_fun_X_58(X0!141, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X)))))))))) <=> ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!141) | (~ip(uri_ex_p1)) | (~ic(X0!141)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!141, uri_ex_p1), tptp_fun_Y_57(X0!141, uri_ex_p1))) | icext(X0!141, tptp_fun_X_58(X0!141, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))))))))))),
% 0.70/0.86 inference(monotonicity,[status(thm)],[221])).
% 0.70/0.86 tff(223,plain,
% 0.70/0.86 (((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!141) | (~ic(X0!141)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!141, uri_ex_p1), tptp_fun_Y_57(X0!141, uri_ex_p1))) | icext(X0!141, tptp_fun_X_58(X0!141, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X)))))))))) <=> ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!141) | (~ip(uri_ex_p1)) | (~ic(X0!141)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!141, uri_ex_p1), tptp_fun_Y_57(X0!141, uri_ex_p1))) | icext(X0!141, tptp_fun_X_58(X0!141, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))))))))))),
% 0.70/0.86 inference(transitivity,[status(thm)],[222, 220])).
% 0.70/0.86 tff(224,plain,
% 0.70/0.86 ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!141) | (~ic(X0!141)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!141, uri_ex_p1), tptp_fun_Y_57(X0!141, uri_ex_p1))) | icext(X0!141, tptp_fun_X_58(X0!141, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X)))))))))),
% 0.70/0.86 inference(quant_inst,[status(thm)],[])).
% 0.70/0.86 tff(225,plain,
% 0.70/0.86 ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!141) | (~ip(uri_ex_p1)) | (~ic(X0!141)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!141, uri_ex_p1), tptp_fun_Y_57(X0!141, uri_ex_p1))) | icext(X0!141, tptp_fun_X_58(X0!141, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X)))))))))),
% 0.70/0.86 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.70/0.86 tff(226,plain,
% 0.70/0.86 (~((~(iext(uri_rdfs_domain, uri_ex_p1, X0!141) | (~ip(uri_ex_p1)) | (~ic(X0!141)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!141, uri_ex_p1), tptp_fun_Y_57(X0!141, uri_ex_p1))) | icext(X0!141, tptp_fun_X_58(X0!141, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))))))))),
% 0.70/0.86 inference(unit_resolution,[status(thm)],[225, 219])).
% 0.70/0.87 tff(227,plain,
% 0.70/0.87 (((~(iext(uri_rdfs_domain, uri_ex_p1, X0!141) | (~ip(uri_ex_p1)) | (~ic(X0!141)) | (~((~iext(uri_ex_p1, tptp_fun_X_58(X0!141, uri_ex_p1), tptp_fun_Y_57(X0!141, uri_ex_p1))) | icext(X0!141, tptp_fun_X_58(X0!141, uri_ex_p1)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X)))))))) | ((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))))))),
% 0.70/0.87 inference(tautology,[status(thm)],[])).
% 0.70/0.87 tff(228,plain,
% 0.70/0.87 ((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X)))))),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.70/0.87 tff(229,plain,
% 0.70/0.87 (iext(uri_rdfs_domain, uri_ex_p1, X0!141)),
% 0.70/0.87 inference(and_elim,[status(thm)],[7])).
% 0.70/0.87 tff(230,plain,
% 0.70/0.87 ((~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))))))) | (~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X)))))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(231,plain,
% 0.71/0.87 ((~((~iext(uri_rdfs_domain, uri_ex_p1, X0!141)) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))))))) | (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X)))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.71/0.87 tff(232,plain,
% 0.71/0.87 (~((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[231, 228])).
% 0.71/0.87 tff(233,plain,
% 0.71/0.87 (((~ic(X0!141)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X)))) | ![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(234,plain,
% 0.71/0.87 (![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.71/0.87 tff(235,plain,
% 0.71/0.87 (((~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))) | ((~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | icext(X0!141, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p)))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | icext(X0!141, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(236,plain,
% 0.71/0.87 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))) | ((~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | icext(X0!141, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(237,plain,
% 0.71/0.87 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | icext(X0!141, X))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | icext(X0!141, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.71/0.87 tff(238,plain,
% 0.71/0.87 (icext(X0!141, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[237, 234, 197])).
% 0.71/0.87 tff(239,plain,
% 0.71/0.87 ((~(icext(X0!141, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p)) <=> (tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_x))) | (~icext(X0!141, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_x)),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(240,plain,
% 0.71/0.87 ((~(icext(X0!141, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p)) <=> (tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_x))) | (tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_x)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.71/0.88 tff(241,plain,
% 0.71/0.88 (tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p) = uri_ex_x),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[240, 195])).
% 0.71/0.88 tff(242,plain,
% 0.71/0.88 (iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)) <=> iext(uri_ex_p, uri_ex_x, uri_ex_y)),
% 0.71/0.88 inference(monotonicity,[status(thm)],[241, 179])).
% 0.71/0.88 tff(243,plain,
% 0.71/0.88 (iext(uri_ex_p, uri_ex_x, uri_ex_y) <=> iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))),
% 0.71/0.88 inference(symmetry,[status(thm)],[242])).
% 0.71/0.88 tff(244,plain,
% 0.71/0.88 (iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[106, 243])).
% 0.71/0.88 tff(245,plain,
% 0.71/0.88 (((~iext(uri_ex_p2, tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p1, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y1_101(uri_ex_p2, uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p)))),
% 0.71/0.88 inference(tautology,[status(thm)],[])).
% 0.71/0.88 tff(246,plain,
% 0.71/0.88 (~iext(uri_ex_p, tptp_fun_Y0_102(uri_ex_p2, uri_ex_p1, uri_ex_p), tptp_fun_Y2_100(uri_ex_p2, uri_ex_p1, uri_ex_p))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[245, 133])).
% 0.71/0.88 tff(247,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[246, 244])).
% 0.71/0.88 % SZS output end Proof
% 0.71/0.89 % E exiting
%------------------------------------------------------------------------------