%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB046+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 05:29:45 AM UTC 2025
% Result : Theorem 0.61s 0.77s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWB046+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 07:54:18 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.61/0.77 % SZS status Theorem
% 0.61/0.77 % SZS output start Proof
% 0.61/0.77 tff(tptp_fun_X2_115_type, type, (
% 0.61/0.77 tptp_fun_X2_115: $i > $i)).
% 0.61/0.77 tff(uri_ex_p_type, type, (
% 0.61/0.77 uri_ex_p: $i)).
% 0.61/0.77 tff(tptp_fun_X1_116_type, type, (
% 0.61/0.77 tptp_fun_X1_116: $i > $i)).
% 0.61/0.77 tff(uri_ex_x_type, type, (
% 0.61/0.77 uri_ex_x: $i)).
% 0.61/0.77 tff(icext_type, type, (
% 0.61/0.77 icext: ( $i * $i ) > $o)).
% 0.61/0.77 tff(tptp_fun_X1_141_type, type, (
% 0.61/0.77 tptp_fun_X1_141: $i)).
% 0.61/0.77 tff(ic_type, type, (
% 0.61/0.77 ic: $i > $o)).
% 0.61/0.77 tff(iext_type, type, (
% 0.61/0.77 iext: ( $i * $i * $i ) > $o)).
% 0.61/0.77 tff(tptp_fun_X0_140_type, type, (
% 0.61/0.77 tptp_fun_X0_140: $i)).
% 0.61/0.77 tff(uri_owl_oneOf_type, type, (
% 0.61/0.77 uri_owl_oneOf: $i)).
% 0.61/0.77 tff(tptp_fun_X_8_type, type, (
% 0.61/0.77 tptp_fun_X_8: ( $i * $i ) > $i)).
% 0.61/0.77 tff(uri_rdf_nil_type, type, (
% 0.61/0.77 uri_rdf_nil: $i)).
% 0.61/0.77 tff(uri_rdf_rest_type, type, (
% 0.61/0.77 uri_rdf_rest: $i)).
% 0.61/0.77 tff(uri_rdfs_domain_type, type, (
% 0.61/0.77 uri_rdfs_domain: $i)).
% 0.61/0.77 tff(uri_ex_y_type, type, (
% 0.61/0.77 uri_ex_y: $i)).
% 0.61/0.77 tff(uri_rdf_first_type, type, (
% 0.61/0.77 uri_rdf_first: $i)).
% 0.61/0.77 tff(tptp_fun_Y_114_type, type, (
% 0.61/0.77 tptp_fun_Y_114: $i > $i)).
% 0.61/0.77 tff(ip_type, type, (
% 0.61/0.77 ip: $i > $o)).
% 0.61/0.77 tff(uri_owl_InverseFunctionalProperty_type, type, (
% 0.61/0.77 uri_owl_InverseFunctionalProperty: $i)).
% 0.61/0.77 tff(uri_rdf_type_type, type, (
% 0.61/0.77 uri_rdf_type: $i)).
% 0.61/0.77 tff(tptp_fun_X_58_type, type, (
% 0.61/0.77 tptp_fun_X_58: ( $i * $i ) > $i)).
% 0.61/0.77 tff(tptp_fun_Y_57_type, type, (
% 0.61/0.77 tptp_fun_Y_57: ( $i * $i ) > $i)).
% 0.61/0.77 tff(1,plain,
% 0.61/0.77 ((uri_ex_x = tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_x)),
% 0.61/0.77 inference(commutativity,[status(thm)],[])).
% 0.61/0.77 tff(2,plain,
% 0.61/0.77 (?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1)) <=> ?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(3,plain,
% 0.61/0.77 (^[X1: $i, X0: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) <=> (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0))), ((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) <=> ((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)))), rewrite(((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) <=> (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y))), ((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) <=> (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y)))), (((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_domain, uri_ex_p, X1)) <=> ((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_domain, uri_ex_p, X1)))), rewrite(((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_domain, uri_ex_p, X1)) <=> (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1))), (((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_domain, uri_ex_p, X1)) <=> (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(4,plain,
% 0.61/0.77 (?[X1: $i, X0: $i] : ((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_domain, uri_ex_p, X1)) <=> ?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[3])).
% 0.61/0.77 tff(5,axiom,(?[X1: $i, X0: $i] : ((((iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_ex_p, uri_ex_x, uri_ex_y)) & iext(uri_rdfs_domain, uri_ex_p, X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','premise_rdfbased_sem_char_inversefunc_ext')).
% 0.61/0.77 tff(6,plain,
% 0.61/0.77 (?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.61/0.77 tff(7,plain,
% 0.61/0.77 (?[X1: $i, X0: $i] : (iext(uri_rdf_first, X0, uri_ex_x) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.61/0.77 tff(8,plain,(
% 0.61/0.77 iext(uri_rdf_first, X0!140, uri_ex_x) & iext(uri_rdf_rest, X0!140, uri_rdf_nil) & iext(uri_owl_oneOf, X1!141, X0!140) & iext(uri_ex_p, uri_ex_x, uri_ex_y) & iext(uri_rdfs_domain, uri_ex_p, X1!141)),
% 0.61/0.77 inference(skolemize,[status(sab)],[7])).
% 0.61/0.77 tff(9,plain,
% 0.61/0.77 (iext(uri_rdf_rest, X0!140, uri_rdf_nil)),
% 0.61/0.77 inference(and_elim,[status(thm)],[8])).
% 0.61/0.77 tff(10,plain,
% 0.61/0.77 (iext(uri_rdf_first, X0!140, uri_ex_x)),
% 0.61/0.77 inference(and_elim,[status(thm)],[8])).
% 0.61/0.77 tff(11,plain,
% 0.61/0.77 (^[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)))))))))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(12,plain,
% 0.61/0.77 (![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))))))))))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[11])).
% 0.61/0.77 tff(13,plain,
% 0.61/0.77 (^[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)))))))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(14,plain,
% 0.61/0.77 (![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))))))))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[13])).
% 0.61/0.77 tff(15,plain,
% 0.61/0.77 (^[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)))))))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(16,plain,
% 0.61/0.77 (![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))))))))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[15])).
% 0.61/0.77 tff(17,plain,
% 0.61/0.77 (![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))))))))),
% 0.61/0.77 inference(transitivity,[status(thm)],[16, 14])).
% 0.61/0.77 tff(18,plain,
% 0.61/0.77 (^[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))))))))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(19,plain,
% 0.61/0.77 (![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))))))))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[18])).
% 0.61/0.77 tff(20,plain,
% 0.61/0.77 (^[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)))))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(21,plain,
% 0.61/0.77 (![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))))))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[20])).
% 0.61/0.77 tff(22,plain,
% 0.61/0.77 (![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)))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(23,plain,
% 0.61/0.77 (^[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)))))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(24,plain,
% 0.61/0.77 (![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)))))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[23])).
% 0.61/0.77 tff(25,axiom,(![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_enum_class_001')).
% 0.61/0.77 tff(26,plain,
% 0.61/0.77 (![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)))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.61/0.77 tff(27,plain,
% 0.61/0.77 (![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)))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.61/0.77 tff(28,plain,(
% 0.61/0.77 ![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)))))))),
% 0.61/0.77 inference(skolemize,[status(sab)],[27])).
% 0.61/0.77 tff(29,plain,
% 0.61/0.77 (![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))))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.61/0.77 tff(30,plain,
% 0.61/0.77 (![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))))))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.61/0.77 tff(31,plain,
% 0.61/0.77 (![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))))))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[30, 17])).
% 0.61/0.77 tff(32,plain,
% 0.61/0.77 (![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))))))))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[31, 12])).
% 0.61/0.77 tff(33,plain,
% 0.61/0.77 (((~![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, X0!140, uri_ex_x)) | (~iext(uri_rdf_rest, X0!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!141, X0!140) | (~ic(X1!141)) | (~(icext(X1!141, tptp_fun_X_8(uri_ex_x, X1!141)) <=> (tptp_fun_X_8(uri_ex_x, X1!141) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!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, X0!140, uri_ex_x)) | (~iext(uri_rdf_rest, X0!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!141, X0!140) | (~ic(X1!141)) | (~(icext(X1!141, tptp_fun_X_8(uri_ex_x, X1!141)) <=> (tptp_fun_X_8(uri_ex_x, X1!141) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))))))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(34,plain,
% 0.61/0.77 ((~![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, X0!140, uri_ex_x)) | (~iext(uri_rdf_rest, X0!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!141, X0!140) | (~ic(X1!141)) | (~(icext(X1!141, tptp_fun_X_8(uri_ex_x, X1!141)) <=> (tptp_fun_X_8(uri_ex_x, X1!141) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))))))))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(35,plain,
% 0.61/0.78 ((~![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, X0!140, uri_ex_x)) | (~iext(uri_rdf_rest, X0!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!141, X0!140) | (~ic(X1!141)) | (~(icext(X1!141, tptp_fun_X_8(uri_ex_x, X1!141)) <=> (tptp_fun_X_8(uri_ex_x, X1!141) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x)))))))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.61/0.78 tff(36,plain,
% 0.61/0.78 (~((~(iext(uri_owl_oneOf, X1!141, X0!140) | (~ic(X1!141)) | (~(icext(X1!141, tptp_fun_X_8(uri_ex_x, X1!141)) <=> (tptp_fun_X_8(uri_ex_x, X1!141) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))))))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[35, 32, 10, 9])).
% 0.61/0.78 tff(37,plain,
% 0.61/0.78 (((~(iext(uri_owl_oneOf, X1!141, X0!140) | (~ic(X1!141)) | (~(icext(X1!141, tptp_fun_X_8(uri_ex_x, X1!141)) <=> (tptp_fun_X_8(uri_ex_x, X1!141) = uri_ex_x))))) | (~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x)))))))) | ((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))))),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(38,plain,
% 0.61/0.78 ((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x)))))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.61/0.78 tff(39,plain,
% 0.61/0.78 (iext(uri_owl_oneOf, X1!141, X0!140)),
% 0.61/0.78 inference(and_elim,[status(thm)],[8])).
% 0.61/0.78 tff(40,plain,
% 0.61/0.78 ((~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))))) | (~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x)))))),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(41,plain,
% 0.61/0.78 ((~((~iext(uri_owl_oneOf, X1!141, X0!140)) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))))) | (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x)))))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.61/0.78 tff(42,plain,
% 0.61/0.78 (~((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.61/0.78 tff(43,plain,
% 0.61/0.78 (((~ic(X1!141)) | (~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x)))) | ![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(44,plain,
% 0.61/0.78 (![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.61/0.78 tff(45,plain,
% 0.61/0.78 ((~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))) | (icext(X1!141, tptp_fun_X1_116(uri_ex_p)) <=> (tptp_fun_X1_116(uri_ex_p) = uri_ex_x))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(46,plain,
% 0.61/0.78 (icext(X1!141, tptp_fun_X1_116(uri_ex_p)) <=> (tptp_fun_X1_116(uri_ex_p) = uri_ex_x)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.61/0.78 tff(47,plain,
% 0.61/0.78 (^[P: $i] : rewrite((~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))) <=> (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(48,plain,
% 0.61/0.78 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))) <=> ![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[47])).
% 0.61/0.78 tff(49,plain,
% 0.61/0.78 (^[P: $i] : refl((~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(50,plain,
% 0.61/0.78 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[49])).
% 0.61/0.78 tff(51,plain,
% 0.61/0.78 (^[P: $i] : rewrite((~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(52,plain,
% 0.61/0.78 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[51])).
% 0.61/0.78 tff(53,plain,
% 0.61/0.78 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 0.61/0.78 inference(transitivity,[status(thm)],[52, 50])).
% 0.61/0.78 tff(54,plain,
% 0.61/0.78 (^[P: $i] : trans(monotonicity(rewrite(((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) <=> ((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))), trans(monotonicity(rewrite((~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P)))) <=> (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))), ((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))), rewrite((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))), ((icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))) <=> (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))), ((((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P)))))) <=> (((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))))), rewrite((((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))), ((((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P)))))) <=> (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(55,plain,
% 0.61/0.78 (![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P)))))) <=> ![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[54])).
% 0.61/0.78 tff(56,plain,
% 0.61/0.78 (^[P: $i] : rewrite((((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))))) <=> (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P)))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(57,plain,
% 0.61/0.78 (![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))))) <=> ![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[56])).
% 0.61/0.78 tff(58,plain,
% 0.61/0.78 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) <=> ![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(59,plain,
% 0.61/0.78 (^[P: $i] : rewrite((icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((iext(P, X1, Y) & iext(P, X2, Y)) => (X1 = X2)))) <=> (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(60,plain,
% 0.61/0.78 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((iext(P, X1, Y) & iext(P, X2, Y)) => (X1 = X2)))) <=> ![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[59])).
% 0.61/0.78 tff(61,axiom,(![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((iext(P, X1, Y) & iext(P, X2, Y)) => (X1 = X2))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_char_inversefunctional')).
% 0.61/0.78 tff(62,plain,
% 0.61/0.78 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.61/0.78 tff(63,plain,
% 0.61/0.78 (![P: $i] : (icext(uri_owl_InverseFunctionalProperty, P) <=> (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.61/0.78 tff(64,plain,(
% 0.61/0.78 ![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | ((~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P)))))))),
% 0.61/0.78 inference(skolemize,[status(sab)],[63])).
% 0.61/0.78 tff(65,plain,
% 0.61/0.78 (![P: $i] : (((~icext(uri_owl_InverseFunctionalProperty, P)) | (ip(P) & ![X1: $i, X2: $i, Y: $i] : ((~(iext(P, X1, Y) & iext(P, X2, Y))) | (X1 = X2)))) & (icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((~(iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P)) & iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))) | (tptp_fun_X1_116(P) = tptp_fun_X2_115(P))))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.61/0.78 tff(66,plain,
% 0.61/0.78 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.61/0.78 tff(67,plain,
% 0.61/0.78 (![P: $i] : (~((~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y)))))))) | (~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P)))))))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[66, 53])).
% 0.61/0.78 tff(68,plain,
% 0.61/0.78 (![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[67, 48])).
% 0.61/0.78 tff(69,plain,
% 0.61/0.78 (((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(70,plain,
% 0.61/0.78 ((~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))) <=> (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(71,plain,
% 0.61/0.78 (((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[70])).
% 0.61/0.78 tff(72,plain,
% 0.61/0.78 (((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))) <=> ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))))),
% 0.61/0.78 inference(transitivity,[status(thm)],[71, 69])).
% 0.61/0.78 tff(73,plain,
% 0.61/0.78 ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(74,plain,
% 0.61/0.78 ((~![P: $i] : (~((~(icext(uri_owl_InverseFunctionalProperty, P) | (~ip(P)) | (~((tptp_fun_X1_116(P) = tptp_fun_X2_115(P)) | (~iext(P, tptp_fun_X1_116(P), tptp_fun_Y_114(P))) | (~iext(P, tptp_fun_X2_115(P), tptp_fun_Y_114(P))))))) | (~((~icext(uri_owl_InverseFunctionalProperty, P)) | (~((~ip(P)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(P, X2, Y)) | (~iext(P, X1, Y))))))))))) | (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.61/0.78 tff(75,plain,
% 0.61/0.78 (~((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y)))))))))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[74, 68])).
% 0.61/0.78 tff(76,plain,
% 0.61/0.78 (((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))) | (~((~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~![X1: $i, X2: $i, Y: $i] : ((X1 = X2) | (~iext(uri_ex_p, X2, Y)) | (~iext(uri_ex_p, X1, Y))))))))) | (icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(77,plain,
% 0.61/0.78 (icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.61/0.78 tff(78,plain,
% 0.61/0.78 (iext(uri_ex_p, uri_ex_x, uri_ex_y)),
% 0.61/0.78 inference(and_elim,[status(thm)],[8])).
% 0.61/0.78 tff(79,plain,
% 0.61/0.78 (^[S: $i, P: $i, O: $i] : refl((ip(P) | (~iext(P, S, O))) <=> (ip(P) | (~iext(P, S, O))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(80,plain,
% 0.61/0.78 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O))) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[79])).
% 0.61/0.78 tff(81,plain,
% 0.61/0.78 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O))) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(82,plain,
% 0.61/0.78 (^[S: $i, P: $i, O: $i] : rewrite((iext(P, S, O) => ip(P)) <=> (ip(P) | (~iext(P, S, O))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(83,plain,
% 0.61/0.78 (![S: $i, P: $i, O: $i] : (iext(P, S, O) => ip(P)) <=> ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[82])).
% 0.61/0.78 tff(84,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')).
% 0.61/0.78 tff(85,plain,
% 0.61/0.78 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.61/0.78 tff(86,plain,
% 0.61/0.78 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.61/0.78 tff(87,plain,(
% 0.61/0.78 ![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.61/0.78 inference(skolemize,[status(sab)],[86])).
% 0.61/0.78 tff(88,plain,
% 0.61/0.78 (![S: $i, P: $i, O: $i] : (ip(P) | (~iext(P, S, O)))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.61/0.78 tff(89,plain,
% 0.61/0.78 (((~![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)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(90,plain,
% 0.61/0.78 ((~![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)))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(91,plain,
% 0.61/0.78 ((~![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))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.61/0.78 tff(92,plain,
% 0.61/0.78 (ip(uri_ex_p)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[91, 88, 78])).
% 0.61/0.78 tff(93,plain,
% 0.61/0.78 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(94,plain,
% 0.61/0.78 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[93])).
% 0.61/0.78 tff(95,plain,
% 0.61/0.78 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(96,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','rdfs_cext_def')).
% 0.61/0.79 tff(97,plain,
% 0.61/0.79 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.61/0.79 tff(98,plain,(
% 0.61/0.79 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.61/0.79 inference(skolemize,[status(sab)],[97])).
% 0.61/0.79 tff(99,plain,
% 0.61/0.79 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.61/0.79 tff(100,plain,
% 0.61/0.79 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(101,plain,
% 0.61/0.79 (iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.61/0.79 tff(102,plain,
% 0.61/0.79 ((~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)) <=> (~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(103,axiom,(~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conclusion_rdfbased_sem_char_inversefunc_ext')).
% 0.61/0.79 tff(104,plain,
% 0.61/0.79 (~iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.61/0.79 tff(105,plain,
% 0.61/0.79 ((~(iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))) | iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) | (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(106,plain,
% 0.61/0.79 ((~(iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) <=> icext(uri_owl_InverseFunctionalProperty, uri_ex_p))) | (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.61/0.79 tff(107,plain,
% 0.61/0.79 (~icext(uri_owl_InverseFunctionalProperty, uri_ex_p)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[106, 101])).
% 0.61/0.79 tff(108,plain,
% 0.61/0.79 ((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))) | icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(109,plain,
% 0.61/0.79 ((~(icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))))) | (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[108, 107, 92])).
% 0.61/0.79 tff(110,plain,
% 0.61/0.79 (~((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[109, 77])).
% 0.61/0.79 tff(111,plain,
% 0.61/0.79 (((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))) | iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(112,plain,
% 0.61/0.79 (iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.61/0.79 tff(113,plain,
% 0.61/0.79 (^[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))))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(114,plain,
% 0.61/0.79 (![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)))))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[113])).
% 0.61/0.79 tff(115,plain,
% 0.61/0.79 (^[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)))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(116,plain,
% 0.61/0.79 (![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))))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[115])).
% 0.61/0.79 tff(117,plain,
% 0.61/0.79 (^[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)))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(118,plain,
% 0.61/0.79 (![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))))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[117])).
% 0.61/0.79 tff(119,plain,
% 0.61/0.79 (![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))))))))),
% 0.61/0.79 inference(transitivity,[status(thm)],[118, 116])).
% 0.61/0.79 tff(120,plain,
% 0.61/0.79 (^[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))))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(121,plain,
% 0.61/0.79 (![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))))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[120])).
% 0.61/0.79 tff(122,plain,
% 0.61/0.79 (^[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)))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(123,plain,
% 0.61/0.79 (![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))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[122])).
% 0.61/0.79 tff(124,plain,
% 0.61/0.79 (![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))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(125,plain,
% 0.61/0.79 (^[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)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(126,plain,
% 0.61/0.79 (![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))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[125])).
% 0.61/0.79 tff(127,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')).
% 0.61/0.79 tff(128,plain,
% 0.61/0.79 (![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))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.61/0.79 tff(129,plain,
% 0.61/0.79 (![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))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.61/0.79 tff(130,plain,(
% 0.61/0.79 ![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)))))))),
% 0.61/0.79 inference(skolemize,[status(sab)],[129])).
% 0.61/0.79 tff(131,plain,
% 0.61/0.79 (![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))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.61/0.79 tff(132,plain,
% 0.61/0.79 (![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))))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[131, 121])).
% 0.61/0.79 tff(133,plain,
% 0.61/0.79 (![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))))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[132, 119])).
% 0.61/0.79 tff(134,plain,
% 0.61/0.79 (![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)))))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[133, 114])).
% 0.61/0.79 tff(135,plain,
% 0.61/0.79 ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_ex_p, X1!141) | (~ic(X1!141)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X_58(X1!141, uri_ex_p), tptp_fun_Y_57(X1!141, uri_ex_p))) | icext(X1!141, tptp_fun_X_58(X1!141, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X)))))))))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(136,plain,
% 0.61/0.79 (~((~(iext(uri_rdfs_domain, uri_ex_p, X1!141) | (~ic(X1!141)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X_58(X1!141, uri_ex_p), tptp_fun_Y_57(X1!141, uri_ex_p))) | icext(X1!141, tptp_fun_X_58(X1!141, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))))))))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.61/0.79 tff(137,plain,
% 0.61/0.79 (((~(iext(uri_rdfs_domain, uri_ex_p, X1!141) | (~ic(X1!141)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p, tptp_fun_X_58(X1!141, uri_ex_p), tptp_fun_Y_57(X1!141, uri_ex_p))) | icext(X1!141, tptp_fun_X_58(X1!141, uri_ex_p)))))) | (~((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X)))))))) | ((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))))))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(138,plain,
% 0.61/0.79 ((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X)))))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.61/0.79 tff(139,plain,
% 0.61/0.79 (iext(uri_rdfs_domain, uri_ex_p, X1!141)),
% 0.61/0.79 inference(and_elim,[status(thm)],[8])).
% 0.61/0.79 tff(140,plain,
% 0.61/0.79 ((~((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))))))) | (~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X)))))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(141,plain,
% 0.61/0.79 ((~((~iext(uri_rdfs_domain, uri_ex_p, X1!141)) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))))))) | (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X)))))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.61/0.79 tff(142,plain,
% 0.61/0.79 (~((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[141, 138])).
% 0.61/0.79 tff(143,plain,
% 0.61/0.79 (((~ic(X1!141)) | (~ip(uri_ex_p)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X)))) | ![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(144,plain,
% 0.61/0.79 (![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.61/0.79 tff(145,plain,
% 0.61/0.79 (((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | ((~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X1_116(uri_ex_p)))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X1_116(uri_ex_p)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(146,plain,
% 0.61/0.79 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | ((~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X1_116(uri_ex_p)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(147,plain,
% 0.61/0.79 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X1_116(uri_ex_p))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.61/0.79 tff(148,plain,
% 0.61/0.79 (icext(X1!141, tptp_fun_X1_116(uri_ex_p))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[147, 144, 112])).
% 0.61/0.79 tff(149,plain,
% 0.61/0.79 ((~(icext(X1!141, tptp_fun_X1_116(uri_ex_p)) <=> (tptp_fun_X1_116(uri_ex_p) = uri_ex_x))) | (~icext(X1!141, tptp_fun_X1_116(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = uri_ex_x)),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(150,plain,
% 0.61/0.79 ((~(icext(X1!141, tptp_fun_X1_116(uri_ex_p)) <=> (tptp_fun_X1_116(uri_ex_p) = uri_ex_x))) | (tptp_fun_X1_116(uri_ex_p) = uri_ex_x)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.61/0.79 tff(151,plain,
% 0.61/0.79 (tptp_fun_X1_116(uri_ex_p) = uri_ex_x),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[150, 46])).
% 0.61/0.79 tff(152,plain,
% 0.61/0.79 ((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) <=> (uri_ex_x = tptp_fun_X2_115(uri_ex_p))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[151])).
% 0.61/0.79 tff(153,plain,
% 0.61/0.79 ((tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_x)),
% 0.61/0.79 inference(transitivity,[status(thm)],[152, 1])).
% 0.61/0.79 tff(154,plain,
% 0.61/0.79 ((tptp_fun_X2_115(uri_ex_p) = uri_ex_x) <=> (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))),
% 0.61/0.79 inference(symmetry,[status(thm)],[153])).
% 0.61/0.79 tff(155,plain,
% 0.61/0.79 ((~![X: $i] : (icext(X1!141, X) <=> (X = uri_ex_x))) | (icext(X1!141, tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_x))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(156,plain,
% 0.61/0.79 (icext(X1!141, tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_x)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[155, 44])).
% 0.61/0.79 tff(157,plain,
% 0.61/0.79 (((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))) | iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(158,plain,
% 0.61/0.79 (iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[157, 110])).
% 0.61/0.79 tff(159,plain,
% 0.61/0.79 (((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | ((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X2_115(uri_ex_p)))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X2_115(uri_ex_p)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(160,plain,
% 0.61/0.79 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | ((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X2_115(uri_ex_p)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(161,plain,
% 0.61/0.79 ((~![X: $i, Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(X1!141, X))) | (~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | icext(X1!141, tptp_fun_X2_115(uri_ex_p))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.61/0.79 tff(162,plain,
% 0.61/0.79 (icext(X1!141, tptp_fun_X2_115(uri_ex_p))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[161, 144, 158])).
% 0.61/0.79 tff(163,plain,
% 0.61/0.79 ((~(icext(X1!141, tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_x))) | (~icext(X1!141, tptp_fun_X2_115(uri_ex_p))) | (tptp_fun_X2_115(uri_ex_p) = uri_ex_x)),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(164,plain,
% 0.61/0.79 ((~(icext(X1!141, tptp_fun_X2_115(uri_ex_p)) <=> (tptp_fun_X2_115(uri_ex_p) = uri_ex_x))) | (tptp_fun_X2_115(uri_ex_p) = uri_ex_x)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.61/0.79 tff(165,plain,
% 0.61/0.79 (tptp_fun_X2_115(uri_ex_p) = uri_ex_x),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[164, 156])).
% 0.61/0.79 tff(166,plain,
% 0.61/0.79 (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[165, 154])).
% 0.61/0.79 tff(167,plain,
% 0.61/0.79 (((~iext(uri_ex_p, tptp_fun_X2_115(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (~iext(uri_ex_p, tptp_fun_X1_116(uri_ex_p), tptp_fun_Y_114(uri_ex_p))) | (tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))) | (~(tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p)))),
% 0.61/0.81 inference(tautology,[status(thm)],[])).
% 0.61/0.81 tff(168,plain,
% 0.61/0.81 (~(tptp_fun_X1_116(uri_ex_p) = tptp_fun_X2_115(uri_ex_p))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[167, 110])).
% 0.61/0.81 tff(169,plain,
% 0.61/0.81 ($false),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[168, 166])).
% 0.61/0.81 % SZS output end Proof
% 0.61/0.82 % E exiting
%------------------------------------------------------------------------------