%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB010+2 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:29:32 AM UTC 2025
% Result : Theorem 1.18s 1.37s
% Output : Proof 1.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWB010+2 : TPTP v9.0.0. Released v5.2.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 07:46:48 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.18/1.37 % SZS status Theorem
% 1.18/1.37 % SZS output start Proof
% 1.18/1.37 tff(iext_type, type, (
% 1.18/1.37 iext: ( $i * $i * $i ) > $o)).
% 1.18/1.37 tff(uri_ex_o_type, type, (
% 1.18/1.37 uri_ex_o: $i)).
% 1.18/1.37 tff(uri_ex_s_type, type, (
% 1.18/1.37 uri_ex_s: $i)).
% 1.18/1.37 tff(uri_ex_p_type, type, (
% 1.18/1.37 uri_ex_p: $i)).
% 1.18/1.37 tff(icext_type, type, (
% 1.18/1.37 icext: ( $i * $i ) > $o)).
% 1.18/1.37 tff(tptp_fun_BNODE_x2_5_type, type, (
% 1.18/1.37 tptp_fun_BNODE_x2_5: $i)).
% 1.18/1.37 tff(tptp_fun_BNODE_x3_4_type, type, (
% 1.18/1.37 tptp_fun_BNODE_x3_4: $i)).
% 1.18/1.37 tff(ic_type, type, (
% 1.18/1.37 ic: $i > $o)).
% 1.18/1.37 tff(uri_owl_complementOf_type, type, (
% 1.18/1.37 uri_owl_complementOf: $i)).
% 1.18/1.37 tff(uri_rdf_nil_type, type, (
% 1.18/1.37 uri_rdf_nil: $i)).
% 1.18/1.37 tff(tptp_fun_BNODE_x4_3_type, type, (
% 1.18/1.37 tptp_fun_BNODE_x4_3: $i)).
% 1.18/1.37 tff(uri_rdf_rest_type, type, (
% 1.18/1.37 uri_rdf_rest: $i)).
% 1.18/1.37 tff(uri_rdf_first_type, type, (
% 1.18/1.37 uri_rdf_first: $i)).
% 1.18/1.37 tff(uri_owl_oneOf_type, type, (
% 1.18/1.37 uri_owl_oneOf: $i)).
% 1.18/1.37 tff(tptp_fun_BNODE_x1_6_type, type, (
% 1.18/1.37 tptp_fun_BNODE_x1_6: $i)).
% 1.18/1.37 tff(uri_owl_allValuesFrom_type, type, (
% 1.18/1.37 uri_owl_allValuesFrom: $i)).
% 1.18/1.37 tff(uri_owl_onProperty_type, type, (
% 1.18/1.37 uri_owl_onProperty: $i)).
% 1.18/1.37 tff(uri_rdf_type_type, type, (
% 1.18/1.37 uri_rdf_type: $i)).
% 1.18/1.37 tff(uri_owl_ObjectProperty_type, type, (
% 1.18/1.37 uri_owl_ObjectProperty: $i)).
% 1.18/1.37 tff(tptp_fun_X_0_type, type, (
% 1.18/1.37 tptp_fun_X_0: ( $i * $i ) > $i)).
% 1.18/1.37 tff(tptp_fun_Y_1_type, type, (
% 1.18/1.37 tptp_fun_Y_1: ( $i * $i * $i ) > $i)).
% 1.18/1.37 tff(tptp_fun_Z_2_type, type, (
% 1.18/1.37 tptp_fun_Z_2: ( $i * $i * $i ) > $i)).
% 1.18/1.37 tff(uri_owl_assertionProperty_type, type, (
% 1.18/1.37 uri_owl_assertionProperty: $i)).
% 1.18/1.37 tff(uri_owl_sourceIndividual_type, type, (
% 1.18/1.37 uri_owl_sourceIndividual: $i)).
% 1.18/1.37 tff(uri_owl_targetIndividual_type, type, (
% 1.18/1.37 uri_owl_targetIndividual: $i)).
% 1.18/1.37 tff(uri_owl_NegativePropertyAssertion_type, type, (
% 1.18/1.37 uri_owl_NegativePropertyAssertion: $i)).
% 1.18/1.37 tff(ir_type, type, (
% 1.18/1.37 ir: $i > $o)).
% 1.18/1.37 tff(ip_type, type, (
% 1.18/1.37 ip: $i > $o)).
% 1.18/1.37 tff(uri_owl_Restriction_type, type, (
% 1.18/1.37 uri_owl_Restriction: $i)).
% 1.18/1.37 tff(1,plain,
% 1.18/1.37 (?[BNODE_x1: $i, BNODE_x2: $i, BNODE_x3: $i, BNODE_x4: $i] : (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4) & iext(uri_rdf_first, BNODE_x4, uri_ex_o) & iext(uri_rdf_rest, BNODE_x4, uri_rdf_nil)) <=> ?[BNODE_x1: $i, BNODE_x2: $i, BNODE_x3: $i, BNODE_x4: $i] : (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4) & iext(uri_rdf_first, BNODE_x4, uri_ex_o) & iext(uri_rdf_rest, BNODE_x4, uri_rdf_nil))),
% 1.18/1.37 inference(rewrite,[status(thm)],[])).
% 1.18/1.37 tff(2,plain,
% 1.18/1.37 (^[BNODE_x1: $i, BNODE_x2: $i, BNODE_x3: $i, BNODE_x4: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1)) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) <=> (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p))), ((((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1)) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) <=> ((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)))), rewrite(((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) <=> (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2))), ((((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1)) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) <=> (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)))), (((((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1)) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)) <=> ((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)))), rewrite(((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)) <=> (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3))), (((((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1)) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)) <=> (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)))), ((((((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1)) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4)) <=> ((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4)))), rewrite(((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4)) <=> (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4))), ((((((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1)) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4)) <=> (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4)))), (((((((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1)) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4)) & iext(uri_rdf_first, BNODE_x4, uri_ex_o)) <=> ((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4)) & iext(uri_rdf_first, BNODE_x4, uri_ex_o)))), rewrite(((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4)) & iext(uri_rdf_first, BNODE_x4, uri_ex_o)) <=> (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4) & iext(uri_rdf_first, BNODE_x4, uri_ex_o))), (((((((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1)) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4)) & iext(uri_rdf_first, BNODE_x4, uri_ex_o)) <=> (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4) & iext(uri_rdf_first, BNODE_x4, uri_ex_o)))), ((((((((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1)) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4)) & iext(uri_rdf_first, BNODE_x4, uri_ex_o)) & iext(uri_rdf_rest, BNODE_x4, uri_rdf_nil)) <=> ((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4) & iext(uri_rdf_first, BNODE_x4, uri_ex_o)) & iext(uri_rdf_rest, BNODE_x4, uri_rdf_nil)))), rewrite(((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4) & iext(uri_rdf_first, BNODE_x4, uri_ex_o)) & iext(uri_rdf_rest, BNODE_x4, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4) & iext(uri_rdf_first, BNODE_x4, uri_ex_o) & iext(uri_rdf_rest, BNODE_x4, uri_rdf_nil))), ((((((((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1)) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4)) & iext(uri_rdf_first, BNODE_x4, uri_ex_o)) & iext(uri_rdf_rest, BNODE_x4, uri_rdf_nil)) <=> (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4) & iext(uri_rdf_first, BNODE_x4, uri_ex_o) & iext(uri_rdf_rest, BNODE_x4, uri_rdf_nil))))),
% 1.18/1.37 inference(bind,[status(th)],[])).
% 1.18/1.37 tff(3,plain,
% 1.18/1.37 (?[BNODE_x1: $i, BNODE_x2: $i, BNODE_x3: $i, BNODE_x4: $i] : (((((((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1)) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4)) & iext(uri_rdf_first, BNODE_x4, uri_ex_o)) & iext(uri_rdf_rest, BNODE_x4, uri_rdf_nil)) <=> ?[BNODE_x1: $i, BNODE_x2: $i, BNODE_x3: $i, BNODE_x4: $i] : (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4) & iext(uri_rdf_first, BNODE_x4, uri_ex_o) & iext(uri_rdf_rest, BNODE_x4, uri_rdf_nil))),
% 1.18/1.37 inference(quant_intro,[status(thm)],[2])).
% 1.18/1.37 tff(4,axiom,(?[BNODE_x1: $i, BNODE_x2: $i, BNODE_x3: $i, BNODE_x4: $i] : (((((((iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1)) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p)) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2)) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3)) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4)) & iext(uri_rdf_first, BNODE_x4, uri_ex_o)) & iext(uri_rdf_rest, BNODE_x4, uri_rdf_nil))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_premise_fullish_010_Negative_Property_Assertions')).
% 1.18/1.37 tff(5,plain,
% 1.18/1.37 (?[BNODE_x1: $i, BNODE_x2: $i, BNODE_x3: $i, BNODE_x4: $i] : (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4) & iext(uri_rdf_first, BNODE_x4, uri_ex_o) & iext(uri_rdf_rest, BNODE_x4, uri_rdf_nil))),
% 1.18/1.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.18/1.37 tff(6,plain,
% 1.18/1.37 (?[BNODE_x1: $i, BNODE_x2: $i, BNODE_x3: $i, BNODE_x4: $i] : (iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1) & iext(uri_owl_onProperty, BNODE_x1, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1, BNODE_x2) & iext(uri_owl_complementOf, BNODE_x2, BNODE_x3) & iext(uri_owl_oneOf, BNODE_x3, BNODE_x4) & iext(uri_rdf_first, BNODE_x4, uri_ex_o) & iext(uri_rdf_rest, BNODE_x4, uri_rdf_nil))),
% 1.18/1.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 1.18/1.37 tff(7,plain,(
% 1.18/1.37 iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1!6) & iext(uri_owl_onProperty, BNODE_x1!6, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1!6, BNODE_x2!5) & iext(uri_owl_complementOf, BNODE_x2!5, BNODE_x3!4) & iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3) & iext(uri_rdf_first, BNODE_x4!3, uri_ex_o) & iext(uri_rdf_rest, BNODE_x4!3, uri_rdf_nil)),
% 1.18/1.37 inference(skolemize,[status(sab)],[6])).
% 1.18/1.37 tff(8,plain,
% 1.18/1.37 (iext(uri_owl_complementOf, BNODE_x2!5, BNODE_x3!4)),
% 1.18/1.37 inference(and_elim,[status(thm)],[7])).
% 1.18/1.37 tff(9,plain,
% 1.18/1.37 (^[Z: $i, C: $i] : refl(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 1.18/1.37 inference(bind,[status(th)],[])).
% 1.18/1.37 tff(10,plain,
% 1.18/1.37 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 1.18/1.37 inference(quant_intro,[status(thm)],[9])).
% 1.18/1.37 tff(11,plain,
% 1.18/1.37 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 1.18/1.37 inference(bind,[status(th)],[])).
% 1.18/1.37 tff(12,plain,
% 1.18/1.37 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 1.18/1.37 inference(quant_intro,[status(thm)],[11])).
% 1.18/1.37 tff(13,plain,
% 1.18/1.37 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 1.18/1.37 inference(transitivity,[status(thm)],[12, 10])).
% 1.18/1.37 tff(14,plain,
% 1.18/1.37 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 1.18/1.37 inference(bind,[status(th)],[])).
% 1.18/1.37 tff(15,plain,
% 1.18/1.37 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 1.18/1.37 inference(quant_intro,[status(thm)],[14])).
% 1.18/1.37 tff(16,plain,
% 1.18/1.37 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 1.18/1.37 inference(rewrite,[status(thm)],[])).
% 1.18/1.37 tff(17,plain,
% 1.18/1.37 (^[Z: $i, C: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(rewrite((icext(Z, X) <=> (~icext(C, X))) <=> (~(icext(C, X) <=> icext(Z, X)))), rewrite((~(icext(C, X) <=> icext(Z, X))) <=> (~(icext(C, X) <=> icext(Z, X)))), ((icext(Z, X) <=> (~icext(C, X))) <=> (~(icext(C, X) <=> icext(Z, X)))))), (![X: $i] : (icext(Z, X) <=> (~icext(C, X))) <=> ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))), (((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))) <=> ((ic(Z) & ic(C)) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), rewrite(((ic(Z) & ic(C)) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) <=> (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))), (((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))) <=> (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), ((iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> (iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))), rewrite((iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), ((iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 1.18/1.37 inference(bind,[status(th)],[])).
% 1.18/1.37 tff(18,plain,
% 1.18/1.37 (![Z: $i, C: $i] : (iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 1.18/1.37 inference(quant_intro,[status(thm)],[17])).
% 1.18/1.37 tff(19,axiom,(![Z: $i, C: $i] : (iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_bool_complementof_class')).
% 1.18/1.37 tff(20,plain,
% 1.18/1.37 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 1.18/1.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.18/1.37 tff(21,plain,
% 1.18/1.37 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 1.18/1.37 inference(modus_ponens,[status(thm)],[20, 16])).
% 1.18/1.37 tff(22,plain,(
% 1.18/1.37 ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 1.18/1.37 inference(skolemize,[status(sab)],[21])).
% 1.18/1.37 tff(23,plain,
% 1.18/1.37 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 1.18/1.37 inference(modus_ponens,[status(thm)],[22, 15])).
% 1.18/1.37 tff(24,plain,
% 1.18/1.37 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 1.18/1.37 inference(modus_ponens,[status(thm)],[23, 13])).
% 1.18/1.37 tff(25,plain,
% 1.18/1.37 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, BNODE_x2!5, BNODE_x3!4)) | (~((~ic(BNODE_x2!5)) | (~ic(BNODE_x3!4)) | (~![X: $i] : (~(icext(BNODE_x3!4, X) <=> icext(BNODE_x2!5, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, BNODE_x2!5, BNODE_x3!4)) | (~((~ic(BNODE_x2!5)) | (~ic(BNODE_x3!4)) | (~![X: $i] : (~(icext(BNODE_x3!4, X) <=> icext(BNODE_x2!5, X)))))))),
% 1.18/1.37 inference(rewrite,[status(thm)],[])).
% 1.18/1.37 tff(26,plain,
% 1.18/1.37 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, BNODE_x2!5, BNODE_x3!4)) | (~((~ic(BNODE_x2!5)) | (~ic(BNODE_x3!4)) | (~![X: $i] : (~(icext(BNODE_x3!4, X) <=> icext(BNODE_x2!5, X)))))))),
% 1.18/1.37 inference(quant_inst,[status(thm)],[])).
% 1.18/1.37 tff(27,plain,
% 1.18/1.37 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(Z)) | (~ic(C)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, BNODE_x2!5, BNODE_x3!4)) | (~((~ic(BNODE_x2!5)) | (~ic(BNODE_x3!4)) | (~![X: $i] : (~(icext(BNODE_x3!4, X) <=> icext(BNODE_x2!5, X))))))),
% 1.18/1.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.18/1.37 tff(28,plain,
% 1.18/1.37 (~((~ic(BNODE_x2!5)) | (~ic(BNODE_x3!4)) | (~![X: $i] : (~(icext(BNODE_x3!4, X) <=> icext(BNODE_x2!5, X)))))),
% 1.18/1.37 inference(unit_resolution,[status(thm)],[27, 24, 8])).
% 1.18/1.37 tff(29,plain,
% 1.18/1.37 (((~ic(BNODE_x2!5)) | (~ic(BNODE_x3!4)) | (~![X: $i] : (~(icext(BNODE_x3!4, X) <=> icext(BNODE_x2!5, X))))) | ![X: $i] : (~(icext(BNODE_x3!4, X) <=> icext(BNODE_x2!5, X)))),
% 1.18/1.37 inference(tautology,[status(thm)],[])).
% 1.18/1.37 tff(30,plain,
% 1.18/1.37 (![X: $i] : (~(icext(BNODE_x3!4, X) <=> icext(BNODE_x2!5, X)))),
% 1.18/1.37 inference(unit_resolution,[status(thm)],[29, 28])).
% 1.18/1.37 tff(31,plain,
% 1.18/1.37 ((~![X: $i] : (~(icext(BNODE_x3!4, X) <=> icext(BNODE_x2!5, X)))) | (~(icext(BNODE_x3!4, uri_ex_o) <=> icext(BNODE_x2!5, uri_ex_o)))),
% 1.18/1.37 inference(quant_inst,[status(thm)],[])).
% 1.18/1.37 tff(32,plain,
% 1.18/1.37 (~(icext(BNODE_x3!4, uri_ex_o) <=> icext(BNODE_x2!5, uri_ex_o))),
% 1.18/1.37 inference(unit_resolution,[status(thm)],[31, 30])).
% 1.18/1.37 tff(33,plain,
% 1.18/1.37 (iext(uri_rdf_rest, BNODE_x4!3, uri_rdf_nil)),
% 1.18/1.37 inference(and_elim,[status(thm)],[7])).
% 1.18/1.37 tff(34,plain,
% 1.18/1.37 (iext(uri_rdf_first, BNODE_x4!3, uri_ex_o)),
% 1.18/1.37 inference(and_elim,[status(thm)],[7])).
% 1.18/1.37 tff(35,plain,
% 1.18/1.37 (^[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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))))))))),
% 1.18/1.37 inference(bind,[status(th)],[])).
% 1.18/1.37 tff(36,plain,
% 1.18/1.37 (![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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 1.18/1.38 inference(quant_intro,[status(thm)],[35])).
% 1.18/1.38 tff(37,plain,
% 1.18/1.38 (^[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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))))),
% 1.18/1.38 inference(bind,[status(th)],[])).
% 1.18/1.38 tff(38,plain,
% 1.18/1.38 (![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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 1.18/1.38 inference(quant_intro,[status(thm)],[37])).
% 1.18/1.38 tff(39,plain,
% 1.18/1.38 (^[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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))))),
% 1.18/1.38 inference(bind,[status(th)],[])).
% 1.18/1.38 tff(40,plain,
% 1.18/1.38 (![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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 1.18/1.38 inference(quant_intro,[status(thm)],[39])).
% 1.18/1.38 tff(41,plain,
% 1.18/1.38 (![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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 1.18/1.38 inference(transitivity,[status(thm)],[40, 38])).
% 1.18/1.38 tff(42,plain,
% 1.18/1.38 (^[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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))) <=> (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))), rewrite((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))))),
% 1.18/1.38 inference(bind,[status(th)],[])).
% 1.18/1.38 tff(43,plain,
% 1.18/1.38 (![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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 1.18/1.38 inference(quant_intro,[status(thm)],[42])).
% 1.18/1.38 tff(44,plain,
% 1.18/1.38 (^[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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))),
% 1.18/1.38 inference(bind,[status(th)],[])).
% 1.18/1.38 tff(45,plain,
% 1.18/1.38 (![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_0(A1, Z)) <=> (tptp_fun_X_0(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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))),
% 1.18/1.38 inference(quant_intro,[status(thm)],[44])).
% 1.18/1.38 tff(46,plain,
% 1.18/1.38 (![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)))))),
% 1.18/1.38 inference(rewrite,[status(thm)],[])).
% 1.18/1.38 tff(47,plain,
% 1.18/1.38 (^[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)))))))),
% 1.18/1.38 inference(bind,[status(th)],[])).
% 1.18/1.38 tff(48,plain,
% 1.18/1.38 (![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)))))),
% 1.18/1.38 inference(quant_intro,[status(thm)],[47])).
% 1.18/1.38 tff(49,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/theBenchmark.p','owl_enum_class_001')).
% 1.18/1.38 tff(50,plain,
% 1.18/1.38 (![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)))))),
% 1.18/1.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.18/1.38 tff(51,plain,
% 1.18/1.38 (![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)))))),
% 1.18/1.38 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.18/1.38 tff(52,plain,(
% 1.18/1.38 ![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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1)))))))),
% 1.18/1.38 inference(skolemize,[status(sab)],[51])).
% 1.18/1.38 tff(53,plain,
% 1.18/1.38 (![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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))),
% 1.18/1.38 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.18/1.38 tff(54,plain,
% 1.18/1.38 (![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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 1.18/1.38 inference(modus_ponens,[status(thm)],[53, 43])).
% 1.18/1.38 tff(55,plain,
% 1.18/1.38 (![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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))))))),
% 1.18/1.38 inference(modus_ponens,[status(thm)],[54, 41])).
% 1.18/1.38 tff(56,plain,
% 1.18/1.38 (![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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 1.18/1.38 inference(modus_ponens,[status(thm)],[55, 36])).
% 1.18/1.38 tff(57,plain,
% 1.18/1.38 (((~![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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, BNODE_x4!3, uri_ex_o)) | (~iext(uri_rdf_rest, BNODE_x4!3, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3) | (~ic(BNODE_x3!4)) | (~(icext(BNODE_x3!4, tptp_fun_X_0(uri_ex_o, BNODE_x3!4)) <=> (tptp_fun_X_0(uri_ex_o, BNODE_x3!4) = uri_ex_o))))) | (~((~iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3)) | (~((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))))))))))) <=> ((~![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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, BNODE_x4!3, uri_ex_o)) | (~iext(uri_rdf_rest, BNODE_x4!3, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3) | (~ic(BNODE_x3!4)) | (~(icext(BNODE_x3!4, tptp_fun_X_0(uri_ex_o, BNODE_x3!4)) <=> (tptp_fun_X_0(uri_ex_o, BNODE_x3!4) = uri_ex_o))))) | (~((~iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3)) | (~((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))))))))))),
% 1.18/1.38 inference(rewrite,[status(thm)],[])).
% 1.18/1.38 tff(58,plain,
% 1.18/1.38 ((~![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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, BNODE_x4!3, uri_ex_o)) | (~iext(uri_rdf_rest, BNODE_x4!3, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3) | (~ic(BNODE_x3!4)) | (~(icext(BNODE_x3!4, tptp_fun_X_0(uri_ex_o, BNODE_x3!4)) <=> (tptp_fun_X_0(uri_ex_o, BNODE_x3!4) = uri_ex_o))))) | (~((~iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3)) | (~((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))))))))))),
% 1.18/1.38 inference(quant_inst,[status(thm)],[])).
% 1.18/1.38 tff(59,plain,
% 1.18/1.38 ((~![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_0(A1, Z)) <=> (tptp_fun_X_0(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, BNODE_x4!3, uri_ex_o)) | (~iext(uri_rdf_rest, BNODE_x4!3, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3) | (~ic(BNODE_x3!4)) | (~(icext(BNODE_x3!4, tptp_fun_X_0(uri_ex_o, BNODE_x3!4)) <=> (tptp_fun_X_0(uri_ex_o, BNODE_x3!4) = uri_ex_o))))) | (~((~iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3)) | (~((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o)))))))))),
% 1.18/1.38 inference(modus_ponens,[status(thm)],[58, 57])).
% 1.18/1.38 tff(60,plain,
% 1.18/1.38 (~((~(iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3) | (~ic(BNODE_x3!4)) | (~(icext(BNODE_x3!4, tptp_fun_X_0(uri_ex_o, BNODE_x3!4)) <=> (tptp_fun_X_0(uri_ex_o, BNODE_x3!4) = uri_ex_o))))) | (~((~iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3)) | (~((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))))))))),
% 1.18/1.38 inference(unit_resolution,[status(thm)],[59, 56, 34, 33])).
% 1.18/1.38 tff(61,plain,
% 1.18/1.38 (((~(iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3) | (~ic(BNODE_x3!4)) | (~(icext(BNODE_x3!4, tptp_fun_X_0(uri_ex_o, BNODE_x3!4)) <=> (tptp_fun_X_0(uri_ex_o, BNODE_x3!4) = uri_ex_o))))) | (~((~iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3)) | (~((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o)))))))) | ((~iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3)) | (~((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))))))),
% 1.18/1.38 inference(tautology,[status(thm)],[])).
% 1.18/1.38 tff(62,plain,
% 1.18/1.38 ((~iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3)) | (~((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o)))))),
% 1.18/1.38 inference(unit_resolution,[status(thm)],[61, 60])).
% 1.18/1.38 tff(63,plain,
% 1.18/1.38 (iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3)),
% 1.18/1.38 inference(and_elim,[status(thm)],[7])).
% 1.18/1.38 tff(64,plain,
% 1.18/1.38 ((~((~iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3)) | (~((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))))))) | (~iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3)) | (~((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o)))))),
% 1.18/1.38 inference(tautology,[status(thm)],[])).
% 1.18/1.38 tff(65,plain,
% 1.18/1.38 ((~((~iext(uri_owl_oneOf, BNODE_x3!4, BNODE_x4!3)) | (~((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))))))) | (~((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o)))))),
% 1.18/1.38 inference(unit_resolution,[status(thm)],[64, 63])).
% 1.18/1.38 tff(66,plain,
% 1.18/1.38 (~((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))))),
% 1.18/1.38 inference(unit_resolution,[status(thm)],[65, 62])).
% 1.18/1.38 tff(67,plain,
% 1.18/1.38 (((~ic(BNODE_x3!4)) | (~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o)))) | ![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))),
% 1.18/1.38 inference(tautology,[status(thm)],[])).
% 1.18/1.38 tff(68,plain,
% 1.18/1.38 (![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))),
% 1.18/1.38 inference(unit_resolution,[status(thm)],[67, 66])).
% 1.18/1.38 tff(69,plain,
% 1.18/1.38 (((~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))) | icext(BNODE_x3!4, uri_ex_o)) <=> ((~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))) | icext(BNODE_x3!4, uri_ex_o))),
% 1.18/1.38 inference(rewrite,[status(thm)],[])).
% 1.18/1.38 tff(70,plain,
% 1.18/1.38 ((icext(BNODE_x3!4, uri_ex_o) <=> $true) <=> icext(BNODE_x3!4, uri_ex_o)),
% 1.18/1.38 inference(rewrite,[status(thm)],[])).
% 1.18/1.38 tff(71,plain,
% 1.18/1.38 ((uri_ex_o = uri_ex_o) <=> $true),
% 1.18/1.38 inference(rewrite,[status(thm)],[])).
% 1.18/1.38 tff(72,plain,
% 1.18/1.38 ((icext(BNODE_x3!4, uri_ex_o) <=> (uri_ex_o = uri_ex_o)) <=> (icext(BNODE_x3!4, uri_ex_o) <=> $true)),
% 1.18/1.38 inference(monotonicity,[status(thm)],[71])).
% 1.18/1.38 tff(73,plain,
% 1.18/1.38 ((icext(BNODE_x3!4, uri_ex_o) <=> (uri_ex_o = uri_ex_o)) <=> icext(BNODE_x3!4, uri_ex_o)),
% 1.18/1.38 inference(transitivity,[status(thm)],[72, 70])).
% 1.18/1.38 tff(74,plain,
% 1.18/1.38 (((~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))) | (icext(BNODE_x3!4, uri_ex_o) <=> (uri_ex_o = uri_ex_o))) <=> ((~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))) | icext(BNODE_x3!4, uri_ex_o))),
% 1.18/1.38 inference(monotonicity,[status(thm)],[73])).
% 1.18/1.38 tff(75,plain,
% 1.18/1.38 (((~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))) | (icext(BNODE_x3!4, uri_ex_o) <=> (uri_ex_o = uri_ex_o))) <=> ((~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))) | icext(BNODE_x3!4, uri_ex_o))),
% 1.18/1.38 inference(transitivity,[status(thm)],[74, 69])).
% 1.18/1.38 tff(76,plain,
% 1.18/1.38 ((~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))) | (icext(BNODE_x3!4, uri_ex_o) <=> (uri_ex_o = uri_ex_o))),
% 1.18/1.38 inference(quant_inst,[status(thm)],[])).
% 1.18/1.38 tff(77,plain,
% 1.18/1.38 ((~![X: $i] : (icext(BNODE_x3!4, X) <=> (X = uri_ex_o))) | icext(BNODE_x3!4, uri_ex_o)),
% 1.18/1.38 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.18/1.38 tff(78,plain,
% 1.18/1.38 (icext(BNODE_x3!4, uri_ex_o)),
% 1.18/1.38 inference(unit_resolution,[status(thm)],[77, 68])).
% 1.18/1.38 tff(79,plain,
% 1.18/1.38 ((icext(BNODE_x3!4, uri_ex_o) <=> icext(BNODE_x2!5, uri_ex_o)) | (~icext(BNODE_x3!4, uri_ex_o)) | (~icext(BNODE_x2!5, uri_ex_o))),
% 1.18/1.38 inference(tautology,[status(thm)],[])).
% 1.18/1.38 tff(80,plain,
% 1.18/1.38 (~icext(BNODE_x2!5, uri_ex_o)),
% 1.18/1.38 inference(unit_resolution,[status(thm)],[79, 78, 32])).
% 1.18/1.38 tff(81,plain,
% 1.18/1.38 (iext(uri_owl_allValuesFrom, BNODE_x1!6, BNODE_x2!5)),
% 1.18/1.38 inference(and_elim,[status(thm)],[7])).
% 1.18/1.38 tff(82,plain,
% 1.18/1.38 (iext(uri_owl_onProperty, BNODE_x1!6, uri_ex_p)),
% 1.18/1.38 inference(and_elim,[status(thm)],[7])).
% 1.18/1.38 tff(83,plain,
% 1.18/1.38 (^[Z: $i, P: $i, C: $i] : refl(((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))))) <=> ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))))))),
% 1.18/1.38 inference(bind,[status(th)],[])).
% 1.18/1.38 tff(84,plain,
% 1.18/1.38 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))))),
% 1.18/1.38 inference(quant_intro,[status(thm)],[83])).
% 1.18/1.38 tff(85,plain,
% 1.18/1.38 (^[Z: $i, P: $i, C: $i] : rewrite(((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))))) <=> ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))))))),
% 1.18/1.38 inference(bind,[status(th)],[])).
% 1.18/1.38 tff(86,plain,
% 1.18/1.38 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))))),
% 1.18/1.38 inference(quant_intro,[status(thm)],[85])).
% 1.18/1.38 tff(87,plain,
% 1.18/1.38 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))))),
% 1.18/1.38 inference(transitivity,[status(thm)],[86, 84])).
% 1.18/1.38 tff(88,plain,
% 1.18/1.38 (^[Z: $i, P: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) <=> (~((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P))))), ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) <=> (~(~((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P))))))), rewrite((~(~((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P))))) <=> ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)))), ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) <=> ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P))))), quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite(((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) <=> ((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))), rewrite((icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))) <=> (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))), ((((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))) <=> (((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))), rewrite((((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))) <=> (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))))), ((((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))) <=> (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))))))), (![X: $i] : (((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))) <=> ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))))), (((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))) <=> (((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))))))), rewrite((((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))))) <=> ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))))), (((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))) <=> ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))))))),
% 1.18/1.38 inference(bind,[status(th)],[])).
% 1.18/1.38 tff(89,plain,
% 1.18/1.38 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P))))))) <=> ![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))))),
% 1.18/1.38 inference(quant_intro,[status(thm)],[88])).
% 1.18/1.38 tff(90,plain,
% 1.18/1.38 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 1.18/1.38 inference(rewrite,[status(thm)],[])).
% 1.18/1.38 tff(91,plain,
% 1.18/1.38 (^[Z: $i, P: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite((icext(Z, X) <=> ![Y: $i] : (iext(P, X, Y) => icext(C, Y))) <=> (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))), (![X: $i] : (icext(Z, X) <=> ![Y: $i] : (iext(P, X, Y) => icext(C, Y))) <=> ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))), (((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ![Y: $i] : (iext(P, X, Y) => icext(C, Y)))) <=> ((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))), rewrite(((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) <=> ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))), (((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ![Y: $i] : (iext(P, X, Y) => icext(C, Y)))) <=> ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))),
% 1.18/1.38 inference(bind,[status(th)],[])).
% 1.18/1.38 tff(92,plain,
% 1.18/1.38 (![Z: $i, P: $i, C: $i] : ((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ![Y: $i] : (iext(P, X, Y) => icext(C, Y)))) <=> ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 1.18/1.38 inference(quant_intro,[status(thm)],[91])).
% 1.18/1.38 tff(93,axiom,(![Z: $i, P: $i, C: $i] : ((iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P)) => ![X: $i] : (icext(Z, X) <=> ![Y: $i] : (iext(P, X, Y) => icext(C, Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_restrict_allvaluesfrom')).
% 1.18/1.38 tff(94,plain,
% 1.18/1.38 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 1.18/1.38 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.18/1.38 tff(95,plain,
% 1.18/1.38 (![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (icext(Z, X) <=> ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 1.18/1.38 inference(modus_ponens,[status(thm)],[94, 90])).
% 1.18/1.38 tff(96,plain,(
% 1.18/1.38 ![Z: $i, P: $i, C: $i] : ((~(iext(uri_owl_allValuesFrom, Z, C) & iext(uri_owl_onProperty, Z, P))) | ![X: $i] : (((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))),
% 1.18/1.38 inference(skolemize,[status(sab)],[95])).
% 1.18/1.38 tff(97,plain,
% 1.18/1.38 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))))),
% 1.18/1.38 inference(modus_ponens,[status(thm)],[96, 89])).
% 1.18/1.38 tff(98,plain,
% 1.18/1.38 (![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))))),
% 1.18/1.38 inference(modus_ponens,[status(thm)],[97, 87])).
% 1.18/1.38 tff(99,plain,
% 1.18/1.38 (((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))))) | ((~iext(uri_owl_allValuesFrom, BNODE_x1!6, BNODE_x2!5)) | (~iext(uri_owl_onProperty, BNODE_x1!6, uri_ex_p)) | ![X: $i] : (~((~((~icext(BNODE_x1!6, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x2!5, Y)))) | (~(icext(BNODE_x1!6, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_1(X, BNODE_x2!5, uri_ex_p))) | icext(BNODE_x2!5, tptp_fun_Y_1(X, BNODE_x2!5, uri_ex_p)))))))))) <=> ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))))) | (~iext(uri_owl_allValuesFrom, BNODE_x1!6, BNODE_x2!5)) | (~iext(uri_owl_onProperty, BNODE_x1!6, uri_ex_p)) | ![X: $i] : (~((~((~icext(BNODE_x1!6, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x2!5, Y)))) | (~(icext(BNODE_x1!6, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_1(X, BNODE_x2!5, uri_ex_p))) | icext(BNODE_x2!5, tptp_fun_Y_1(X, BNODE_x2!5, uri_ex_p)))))))))),
% 1.18/1.38 inference(rewrite,[status(thm)],[])).
% 1.18/1.38 tff(100,plain,
% 1.18/1.38 ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))))) | ((~iext(uri_owl_allValuesFrom, BNODE_x1!6, BNODE_x2!5)) | (~iext(uri_owl_onProperty, BNODE_x1!6, uri_ex_p)) | ![X: $i] : (~((~((~icext(BNODE_x1!6, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x2!5, Y)))) | (~(icext(BNODE_x1!6, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_1(X, BNODE_x2!5, uri_ex_p))) | icext(BNODE_x2!5, tptp_fun_Y_1(X, BNODE_x2!5, uri_ex_p)))))))))),
% 1.18/1.39 inference(quant_inst,[status(thm)],[])).
% 1.18/1.39 tff(101,plain,
% 1.18/1.39 ((~![Z: $i, P: $i, C: $i] : ((~iext(uri_owl_allValuesFrom, Z, C)) | (~iext(uri_owl_onProperty, Z, P)) | ![X: $i] : (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_1(X, C, P))) | icext(C, tptp_fun_Y_1(X, C, P)))))))))) | (~iext(uri_owl_allValuesFrom, BNODE_x1!6, BNODE_x2!5)) | (~iext(uri_owl_onProperty, BNODE_x1!6, uri_ex_p)) | ![X: $i] : (~((~((~icext(BNODE_x1!6, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x2!5, Y)))) | (~(icext(BNODE_x1!6, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_1(X, BNODE_x2!5, uri_ex_p))) | icext(BNODE_x2!5, tptp_fun_Y_1(X, BNODE_x2!5, uri_ex_p))))))))),
% 1.18/1.39 inference(modus_ponens,[status(thm)],[100, 99])).
% 1.18/1.39 tff(102,plain,
% 1.18/1.39 (![X: $i] : (~((~((~icext(BNODE_x1!6, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x2!5, Y)))) | (~(icext(BNODE_x1!6, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_1(X, BNODE_x2!5, uri_ex_p))) | icext(BNODE_x2!5, tptp_fun_Y_1(X, BNODE_x2!5, uri_ex_p))))))))),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[101, 98, 82, 81])).
% 1.18/1.39 tff(103,plain,
% 1.18/1.39 ((~![X: $i] : (~((~((~icext(BNODE_x1!6, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x2!5, Y)))) | (~(icext(BNODE_x1!6, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_1(X, BNODE_x2!5, uri_ex_p))) | icext(BNODE_x2!5, tptp_fun_Y_1(X, BNODE_x2!5, uri_ex_p))))))))) | (~((~((~icext(BNODE_x1!6, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y)))) | (~(icext(BNODE_x1!6, uri_ex_s) | (~((~iext(uri_ex_p, uri_ex_s, tptp_fun_Y_1(uri_ex_s, BNODE_x2!5, uri_ex_p))) | icext(BNODE_x2!5, tptp_fun_Y_1(uri_ex_s, BNODE_x2!5, uri_ex_p))))))))),
% 1.18/1.39 inference(quant_inst,[status(thm)],[])).
% 1.18/1.39 tff(104,plain,
% 1.18/1.39 (~((~((~icext(BNODE_x1!6, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y)))) | (~(icext(BNODE_x1!6, uri_ex_s) | (~((~iext(uri_ex_p, uri_ex_s, tptp_fun_Y_1(uri_ex_s, BNODE_x2!5, uri_ex_p))) | icext(BNODE_x2!5, tptp_fun_Y_1(uri_ex_s, BNODE_x2!5, uri_ex_p)))))))),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[103, 102])).
% 1.18/1.39 tff(105,plain,
% 1.18/1.39 (((~((~icext(BNODE_x1!6, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y)))) | (~(icext(BNODE_x1!6, uri_ex_s) | (~((~iext(uri_ex_p, uri_ex_s, tptp_fun_Y_1(uri_ex_s, BNODE_x2!5, uri_ex_p))) | icext(BNODE_x2!5, tptp_fun_Y_1(uri_ex_s, BNODE_x2!5, uri_ex_p))))))) | ((~icext(BNODE_x1!6, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y)))),
% 1.18/1.39 inference(tautology,[status(thm)],[])).
% 1.18/1.39 tff(106,plain,
% 1.18/1.39 ((~icext(BNODE_x1!6, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y))),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[105, 104])).
% 1.18/1.39 tff(107,plain,
% 1.18/1.39 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 1.18/1.39 inference(bind,[status(th)],[])).
% 1.18/1.39 tff(108,plain,
% 1.18/1.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 1.18/1.39 inference(quant_intro,[status(thm)],[107])).
% 1.18/1.39 tff(109,plain,
% 1.18/1.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 1.18/1.39 inference(rewrite,[status(thm)],[])).
% 1.18/1.39 tff(110,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rdfs_cext_def')).
% 1.18/1.39 tff(111,plain,
% 1.18/1.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 1.18/1.39 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.18/1.39 tff(112,plain,(
% 1.18/1.39 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 1.18/1.39 inference(skolemize,[status(sab)],[111])).
% 1.18/1.39 tff(113,plain,
% 1.18/1.39 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 1.18/1.39 inference(modus_ponens,[status(thm)],[112, 108])).
% 1.18/1.39 tff(114,plain,
% 1.18/1.39 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_s, BNODE_x1!6) <=> icext(BNODE_x1!6, uri_ex_s))),
% 1.18/1.39 inference(quant_inst,[status(thm)],[])).
% 1.18/1.39 tff(115,plain,
% 1.18/1.39 (iext(uri_rdf_type, uri_ex_s, BNODE_x1!6) <=> icext(BNODE_x1!6, uri_ex_s)),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[114, 113])).
% 1.18/1.39 tff(116,plain,
% 1.18/1.39 (iext(uri_rdf_type, uri_ex_s, BNODE_x1!6)),
% 1.18/1.39 inference(and_elim,[status(thm)],[7])).
% 1.18/1.39 tff(117,plain,
% 1.18/1.39 ((~(iext(uri_rdf_type, uri_ex_s, BNODE_x1!6) <=> icext(BNODE_x1!6, uri_ex_s))) | (~iext(uri_rdf_type, uri_ex_s, BNODE_x1!6)) | icext(BNODE_x1!6, uri_ex_s)),
% 1.18/1.39 inference(tautology,[status(thm)],[])).
% 1.18/1.39 tff(118,plain,
% 1.18/1.39 ((~(iext(uri_rdf_type, uri_ex_s, BNODE_x1!6) <=> icext(BNODE_x1!6, uri_ex_s))) | icext(BNODE_x1!6, uri_ex_s)),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[117, 116])).
% 1.18/1.39 tff(119,plain,
% 1.18/1.39 (icext(BNODE_x1!6, uri_ex_s)),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[118, 115])).
% 1.18/1.39 tff(120,plain,
% 1.18/1.39 ((~((~icext(BNODE_x1!6, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y)))) | (~icext(BNODE_x1!6, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y))),
% 1.18/1.39 inference(tautology,[status(thm)],[])).
% 1.18/1.39 tff(121,plain,
% 1.18/1.39 ((~((~icext(BNODE_x1!6, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y)))) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y))),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[120, 119])).
% 1.18/1.39 tff(122,plain,
% 1.18/1.39 (![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y))),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[121, 106])).
% 1.18/1.39 tff(123,plain,
% 1.18/1.39 (((~![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y))) | ((~iext(uri_ex_p, uri_ex_s, uri_ex_o)) | icext(BNODE_x2!5, uri_ex_o))) <=> ((~![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y))) | (~iext(uri_ex_p, uri_ex_s, uri_ex_o)) | icext(BNODE_x2!5, uri_ex_o))),
% 1.18/1.39 inference(rewrite,[status(thm)],[])).
% 1.18/1.39 tff(124,plain,
% 1.18/1.39 ((~![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y))) | ((~iext(uri_ex_p, uri_ex_s, uri_ex_o)) | icext(BNODE_x2!5, uri_ex_o))),
% 1.18/1.39 inference(quant_inst,[status(thm)],[])).
% 1.18/1.39 tff(125,plain,
% 1.18/1.39 ((~![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!5, Y))) | (~iext(uri_ex_p, uri_ex_s, uri_ex_o)) | icext(BNODE_x2!5, uri_ex_o)),
% 1.18/1.39 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.18/1.39 tff(126,plain,
% 1.18/1.39 ((~iext(uri_ex_p, uri_ex_s, uri_ex_o)) | icext(BNODE_x2!5, uri_ex_o)),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[125, 122])).
% 1.18/1.39 tff(127,plain,
% 1.18/1.39 (~iext(uri_ex_p, uri_ex_s, uri_ex_o)),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[126, 80])).
% 1.18/1.39 tff(128,assumption,(~((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)))), introduced(assumption)).
% 1.18/1.39 tff(129,plain,
% 1.18/1.39 (((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p))) | iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)),
% 1.18/1.39 inference(tautology,[status(thm)],[])).
% 1.18/1.39 tff(130,plain,
% 1.18/1.39 (iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[129, 128])).
% 1.18/1.39 tff(131,plain,
% 1.18/1.39 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y))))) <=> ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y))))))),
% 1.18/1.39 inference(bind,[status(th)],[])).
% 1.18/1.39 tff(132,plain,
% 1.18/1.39 (![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y)))))),
% 1.18/1.39 inference(quant_intro,[status(thm)],[131])).
% 1.18/1.39 tff(133,plain,
% 1.18/1.39 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_sourceIndividual, X, Y)) | (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y))) <=> ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y))))))),
% 1.18/1.39 inference(bind,[status(th)],[])).
% 1.18/1.39 tff(134,plain,
% 1.18/1.39 (![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y)))))),
% 1.18/1.39 inference(quant_intro,[status(thm)],[133])).
% 1.18/1.39 tff(135,plain,
% 1.18/1.39 (![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y)))),
% 1.18/1.39 inference(rewrite,[status(thm)],[])).
% 1.18/1.39 tff(136,plain,
% 1.18/1.39 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_sourceIndividual, X, Y) => (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y))) <=> ((~iext(uri_owl_sourceIndividual, X, Y)) | (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y))))),
% 1.18/1.39 inference(bind,[status(th)],[])).
% 1.18/1.39 tff(137,plain,
% 1.18/1.39 (![X: $i, Y: $i] : (iext(uri_owl_sourceIndividual, X, Y) => (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y)))),
% 1.18/1.39 inference(quant_intro,[status(thm)],[136])).
% 1.18/1.39 tff(138,axiom,(![X: $i, Y: $i] : (iext(uri_owl_sourceIndividual, X, Y) => (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_prop_sourceindividual_ext')).
% 1.18/1.39 tff(139,plain,
% 1.18/1.39 (![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y)))),
% 1.18/1.39 inference(modus_ponens,[status(thm)],[138, 137])).
% 1.18/1.39 tff(140,plain,
% 1.18/1.39 (![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y)))),
% 1.18/1.39 inference(modus_ponens,[status(thm)],[139, 135])).
% 1.18/1.39 tff(141,plain,(
% 1.18/1.39 ![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y)))),
% 1.18/1.39 inference(skolemize,[status(sab)],[140])).
% 1.18/1.39 tff(142,plain,
% 1.18/1.39 (![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y)))))),
% 1.18/1.39 inference(modus_ponens,[status(thm)],[141, 134])).
% 1.18/1.39 tff(143,plain,
% 1.18/1.39 (![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y)))))),
% 1.18/1.39 inference(modus_ponens,[status(thm)],[142, 132])).
% 1.18/1.39 tff(144,plain,
% 1.18/1.39 (((~![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y)))))) | ((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p))))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y)))))) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p))))))),
% 1.18/1.39 inference(rewrite,[status(thm)],[])).
% 1.18/1.39 tff(145,plain,
% 1.18/1.39 (((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p))) | (~ir(uri_ex_s))))) <=> ((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p))))))),
% 1.18/1.39 inference(rewrite,[status(thm)],[])).
% 1.18/1.39 tff(146,plain,
% 1.18/1.39 (((~![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y)))))) | ((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p))) | (~ir(uri_ex_s)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y)))))) | ((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p)))))))),
% 1.18/1.39 inference(monotonicity,[status(thm)],[145])).
% 1.18/1.39 tff(147,plain,
% 1.18/1.39 (((~![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y)))))) | ((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p))) | (~ir(uri_ex_s)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y)))))) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p))))))),
% 1.18/1.39 inference(transitivity,[status(thm)],[146, 144])).
% 1.18/1.39 tff(148,plain,
% 1.18/1.39 ((~![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y)))))) | ((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p))) | (~ir(uri_ex_s)))))),
% 1.18/1.39 inference(quant_inst,[status(thm)],[])).
% 1.18/1.39 tff(149,plain,
% 1.18/1.39 ((~![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~icext(uri_owl_NegativePropertyAssertion, X)) | (~ir(Y)))))) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p)))))),
% 1.18/1.39 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.18/1.39 tff(150,plain,
% 1.18/1.39 (~((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p))))),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[149, 143, 130])).
% 1.18/1.39 tff(151,assumption,(~(iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion) <=> icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p)))), introduced(assumption)).
% 1.18/1.39 tff(152,plain,
% 1.18/1.39 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion) <=> icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p)))),
% 1.18/1.39 inference(quant_inst,[status(thm)],[])).
% 1.18/1.39 tff(153,plain,
% 1.18/1.39 ($false),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[152, 113, 151])).
% 1.18/1.39 tff(154,plain,(iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion) <=> icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.39 tff(155,plain,
% 1.18/1.39 (((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p))) | iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)),
% 1.18/1.39 inference(tautology,[status(thm)],[])).
% 1.18/1.39 tff(156,plain,
% 1.18/1.39 (iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[155, 128])).
% 1.18/1.39 tff(157,plain,
% 1.18/1.39 (((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p))) | iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)),
% 1.18/1.39 inference(tautology,[status(thm)],[])).
% 1.18/1.39 tff(158,plain,
% 1.18/1.39 (iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)),
% 1.18/1.39 inference(unit_resolution,[status(thm)],[157, 128])).
% 1.18/1.39 tff(159,plain,
% 1.18/1.39 (^[BNODE_z: $i] : refl(((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))) <=> ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))))),
% 1.18/1.39 inference(bind,[status(th)],[])).
% 1.18/1.39 tff(160,plain,
% 1.18/1.39 (![BNODE_z: $i] : ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))) <=> ![BNODE_z: $i] : ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))),
% 1.18/1.39 inference(quant_intro,[status(thm)],[159])).
% 1.18/1.39 tff(161,plain,
% 1.18/1.39 (^[BNODE_z: $i] : trans(monotonicity(rewrite((iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)) <=> (~((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))))), ((~(iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))) <=> (~(~((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))))))), rewrite((~(~((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))))) <=> ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))), ((~(iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))) <=> ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))))),
% 1.18/1.39 inference(bind,[status(th)],[])).
% 1.18/1.39 tff(162,plain,
% 1.18/1.39 (![BNODE_z: $i] : (~(iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))) <=> ![BNODE_z: $i] : ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))),
% 1.18/1.39 inference(quant_intro,[status(thm)],[161])).
% 1.18/1.39 tff(163,plain,
% 1.18/1.39 ((~?[BNODE_z: $i] : (iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))) <=> (~?[BNODE_z: $i] : (iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))),
% 1.24/1.39 inference(rewrite,[status(thm)],[])).
% 1.24/1.39 tff(164,plain,
% 1.24/1.39 ((~?[BNODE_z: $i] : (((iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))) <=> (~?[BNODE_z: $i] : (iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))),
% 1.24/1.39 inference(rewrite,[status(thm)],[])).
% 1.24/1.39 tff(165,axiom,(~?[BNODE_z: $i] : (((iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_conclusion_fullish_010_Negative_Property_Assertions')).
% 1.24/1.39 tff(166,plain,
% 1.24/1.39 (~?[BNODE_z: $i] : (iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))),
% 1.24/1.39 inference(modus_ponens,[status(thm)],[165, 164])).
% 1.24/1.39 tff(167,plain,
% 1.24/1.39 (~?[BNODE_z: $i] : (iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))),
% 1.24/1.39 inference(modus_ponens,[status(thm)],[166, 163])).
% 1.24/1.39 tff(168,plain,
% 1.24/1.39 (~?[BNODE_z: $i] : (iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))),
% 1.24/1.39 inference(modus_ponens,[status(thm)],[167, 163])).
% 1.24/1.39 tff(169,plain,
% 1.24/1.39 (~?[BNODE_z: $i] : (iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))),
% 1.24/1.39 inference(modus_ponens,[status(thm)],[168, 163])).
% 1.24/1.39 tff(170,plain,
% 1.24/1.39 (^[BNODE_z: $i] : refl($oeq((~(iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o))), (~(iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))))),
% 1.24/1.39 inference(bind,[status(th)],[])).
% 1.24/1.39 tff(171,plain,(
% 1.24/1.39 ![BNODE_z: $i] : (~(iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion) & iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s) & iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p) & iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))),
% 1.24/1.39 inference(nnf-neg,[status(sab)],[169, 170])).
% 1.24/1.39 tff(172,plain,
% 1.24/1.39 (![BNODE_z: $i] : ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))),
% 1.24/1.39 inference(modus_ponens,[status(thm)],[171, 162])).
% 1.24/1.39 tff(173,plain,
% 1.24/1.39 (![BNODE_z: $i] : ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))),
% 1.24/1.39 inference(modus_ponens,[status(thm)],[172, 160])).
% 1.24/1.39 tff(174,plain,
% 1.24/1.39 (((~![BNODE_z: $i] : ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))) | ((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)))) <=> ((~![BNODE_z: $i] : ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)))),
% 1.24/1.39 inference(rewrite,[status(thm)],[])).
% 1.24/1.39 tff(175,plain,
% 1.24/1.39 (((~iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o))) <=> ((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)))),
% 1.24/1.39 inference(rewrite,[status(thm)],[])).
% 1.24/1.39 tff(176,plain,
% 1.24/1.39 (((~![BNODE_z: $i] : ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))) | ((~iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)))) <=> ((~![BNODE_z: $i] : ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))) | ((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion))))),
% 1.24/1.39 inference(monotonicity,[status(thm)],[175])).
% 1.24/1.39 tff(177,plain,
% 1.24/1.39 (((~![BNODE_z: $i] : ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))) | ((~iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)))) <=> ((~![BNODE_z: $i] : ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)))),
% 1.24/1.39 inference(transitivity,[status(thm)],[176, 174])).
% 1.24/1.39 tff(178,plain,
% 1.24/1.39 ((~![BNODE_z: $i] : ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))) | ((~iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)))),
% 1.24/1.39 inference(quant_inst,[status(thm)],[])).
% 1.24/1.39 tff(179,plain,
% 1.24/1.39 ((~![BNODE_z: $i] : ((~iext(uri_rdf_type, BNODE_z, uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, BNODE_z, uri_ex_s)) | (~iext(uri_owl_assertionProperty, BNODE_z, uri_ex_p)) | (~iext(uri_owl_targetIndividual, BNODE_z, uri_ex_o)))) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion))),
% 1.24/1.39 inference(modus_ponens,[status(thm)],[178, 177])).
% 1.24/1.39 tff(180,plain,
% 1.24/1.39 (~iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)),
% 1.24/1.39 inference(unit_resolution,[status(thm)],[179, 173, 158, 130, 156])).
% 1.24/1.39 tff(181,plain,
% 1.24/1.39 ((~(iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion) <=> icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p)))) | iext(uri_rdf_type, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p)))),
% 1.24/1.39 inference(tautology,[status(thm)],[])).
% 1.24/1.39 tff(182,plain,
% 1.24/1.39 (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p))),
% 1.24/1.39 inference(unit_resolution,[status(thm)],[181, 180, 154])).
% 1.24/1.39 tff(183,plain,
% 1.24/1.39 (((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p)))) | icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p))),
% 1.24/1.39 inference(tautology,[status(thm)],[])).
% 1.24/1.39 tff(184,plain,
% 1.24/1.39 ($false),
% 1.24/1.39 inference(unit_resolution,[status(thm)],[183, 182, 150])).
% 1.24/1.39 tff(185,plain,((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.39 tff(186,assumption,(~ir(uri_ex_s)), introduced(assumption)).
% 1.24/1.39 tff(187,plain,
% 1.24/1.39 (^[X: $i] : refl(ir(X) <=> ir(X))),
% 1.24/1.39 inference(bind,[status(th)],[])).
% 1.24/1.39 tff(188,plain,
% 1.24/1.39 (![X: $i] : ir(X) <=> ![X: $i] : ir(X)),
% 1.24/1.39 inference(quant_intro,[status(thm)],[187])).
% 1.24/1.39 tff(189,plain,
% 1.24/1.39 (![X: $i] : ir(X) <=> ![X: $i] : ir(X)),
% 1.24/1.39 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(190,axiom,(![X: $i] : ir(X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','simple_ir')).
% 1.24/1.40 tff(191,plain,
% 1.24/1.40 (![X: $i] : ir(X)),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[190, 189])).
% 1.24/1.40 tff(192,plain,(
% 1.24/1.40 ![X: $i] : ir(X)),
% 1.24/1.40 inference(skolemize,[status(sab)],[191])).
% 1.24/1.40 tff(193,plain,
% 1.24/1.40 (![X: $i] : ir(X)),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[192, 188])).
% 1.24/1.40 tff(194,plain,
% 1.24/1.40 ((~![X: $i] : ir(X)) | ir(uri_ex_s)),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(195,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[194, 193, 186])).
% 1.24/1.40 tff(196,plain,(ir(uri_ex_s)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(197,assumption,(~ir(uri_ex_o)), introduced(assumption)).
% 1.24/1.40 tff(198,plain,
% 1.24/1.40 ((~![X: $i] : ir(X)) | ir(uri_ex_o)),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(199,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[198, 193, 197])).
% 1.24/1.40 tff(200,plain,(ir(uri_ex_o)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(201,plain,
% 1.24/1.40 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_onProperty, X, Y)) | (~((~icext(uri_owl_Restriction, X)) | (~ip(Y))))) <=> ((~iext(uri_owl_onProperty, X, Y)) | (~((~icext(uri_owl_Restriction, X)) | (~ip(Y))))))),
% 1.24/1.40 inference(bind,[status(th)],[])).
% 1.24/1.40 tff(202,plain,
% 1.24/1.40 (![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~icext(uri_owl_Restriction, X)) | (~ip(Y))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~icext(uri_owl_Restriction, X)) | (~ip(Y)))))),
% 1.24/1.40 inference(quant_intro,[status(thm)],[201])).
% 1.24/1.40 tff(203,plain,
% 1.24/1.40 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_onProperty, X, Y)) | (icext(uri_owl_Restriction, X) & ip(Y))) <=> ((~iext(uri_owl_onProperty, X, Y)) | (~((~icext(uri_owl_Restriction, X)) | (~ip(Y))))))),
% 1.24/1.40 inference(bind,[status(th)],[])).
% 1.24/1.40 tff(204,plain,
% 1.24/1.40 (![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (icext(uri_owl_Restriction, X) & ip(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~icext(uri_owl_Restriction, X)) | (~ip(Y)))))),
% 1.24/1.40 inference(quant_intro,[status(thm)],[203])).
% 1.24/1.40 tff(205,plain,
% 1.24/1.40 (![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (icext(uri_owl_Restriction, X) & ip(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (icext(uri_owl_Restriction, X) & ip(Y)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(206,plain,
% 1.24/1.40 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_onProperty, X, Y) => (icext(uri_owl_Restriction, X) & ip(Y))) <=> ((~iext(uri_owl_onProperty, X, Y)) | (icext(uri_owl_Restriction, X) & ip(Y))))),
% 1.24/1.40 inference(bind,[status(th)],[])).
% 1.24/1.40 tff(207,plain,
% 1.24/1.40 (![X: $i, Y: $i] : (iext(uri_owl_onProperty, X, Y) => (icext(uri_owl_Restriction, X) & ip(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (icext(uri_owl_Restriction, X) & ip(Y)))),
% 1.24/1.40 inference(quant_intro,[status(thm)],[206])).
% 1.24/1.40 tff(208,axiom,(![X: $i, Y: $i] : (iext(uri_owl_onProperty, X, Y) => (icext(uri_owl_Restriction, X) & ip(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_prop_onproperty_ext')).
% 1.24/1.40 tff(209,plain,
% 1.24/1.40 (![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (icext(uri_owl_Restriction, X) & ip(Y)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[208, 207])).
% 1.24/1.40 tff(210,plain,
% 1.24/1.40 (![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (icext(uri_owl_Restriction, X) & ip(Y)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[209, 205])).
% 1.24/1.40 tff(211,plain,(
% 1.24/1.40 ![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (icext(uri_owl_Restriction, X) & ip(Y)))),
% 1.24/1.40 inference(skolemize,[status(sab)],[210])).
% 1.24/1.40 tff(212,plain,
% 1.24/1.40 (![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~icext(uri_owl_Restriction, X)) | (~ip(Y)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[211, 204])).
% 1.24/1.40 tff(213,plain,
% 1.24/1.40 (![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~icext(uri_owl_Restriction, X)) | (~ip(Y)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[212, 202])).
% 1.24/1.40 tff(214,plain,
% 1.24/1.40 (((~![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~icext(uri_owl_Restriction, X)) | (~ip(Y)))))) | ((~iext(uri_owl_onProperty, BNODE_x1!6, uri_ex_p)) | (~((~icext(uri_owl_Restriction, BNODE_x1!6)) | (~ip(uri_ex_p)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~icext(uri_owl_Restriction, X)) | (~ip(Y)))))) | (~iext(uri_owl_onProperty, BNODE_x1!6, uri_ex_p)) | (~((~icext(uri_owl_Restriction, BNODE_x1!6)) | (~ip(uri_ex_p)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(215,plain,
% 1.24/1.40 ((~![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~icext(uri_owl_Restriction, X)) | (~ip(Y)))))) | ((~iext(uri_owl_onProperty, BNODE_x1!6, uri_ex_p)) | (~((~icext(uri_owl_Restriction, BNODE_x1!6)) | (~ip(uri_ex_p)))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(216,plain,
% 1.24/1.40 ((~![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~icext(uri_owl_Restriction, X)) | (~ip(Y)))))) | (~iext(uri_owl_onProperty, BNODE_x1!6, uri_ex_p)) | (~((~icext(uri_owl_Restriction, BNODE_x1!6)) | (~ip(uri_ex_p))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.24/1.40 tff(217,plain,
% 1.24/1.40 (~((~icext(uri_owl_Restriction, BNODE_x1!6)) | (~ip(uri_ex_p)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[216, 213, 82])).
% 1.24/1.40 tff(218,plain,
% 1.24/1.40 (((~icext(uri_owl_Restriction, BNODE_x1!6)) | (~ip(uri_ex_p))) | ip(uri_ex_p)),
% 1.24/1.40 inference(tautology,[status(thm)],[])).
% 1.24/1.40 tff(219,plain,
% 1.24/1.40 (ip(uri_ex_p)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[218, 217])).
% 1.24/1.40 tff(220,plain,
% 1.24/1.40 (^[P: $i, A1: $i, A2: $i] : refl((iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2))))) <=> (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2))))))),
% 1.24/1.40 inference(bind,[status(th)],[])).
% 1.24/1.40 tff(221,plain,
% 1.24/1.40 (![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2))))) <=> ![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))),
% 1.24/1.40 inference(quant_intro,[status(thm)],[220])).
% 1.24/1.40 tff(222,plain,
% 1.24/1.40 (^[P: $i, A1: $i, A2: $i] : trans(monotonicity(trans(monotonicity(rewrite((ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2))) <=> (~(iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P))))), ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) <=> (~(~(iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P))))))), rewrite((~(~(iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P))))) <=> (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)))), ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) <=> (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P))))), rewrite((iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1) & iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P) & iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)) <=> (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2))))), (((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | (iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1) & iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P) & iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2))) <=> ((iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P))) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2))))))), rewrite(((iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P))) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2))))) <=> (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))), (((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | (iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1) & iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P) & iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2))) <=> (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))))),
% 1.24/1.40 inference(bind,[status(th)],[])).
% 1.24/1.40 tff(223,plain,
% 1.24/1.40 (![P: $i, A1: $i, A2: $i] : ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | (iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1) & iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P) & iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2))) <=> ![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))),
% 1.24/1.40 inference(quant_intro,[status(thm)],[222])).
% 1.24/1.40 tff(224,plain,
% 1.24/1.40 (![P: $i, A1: $i, A2: $i] : ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | ?[Z: $i] : (iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P) & iext(uri_owl_targetIndividual, Z, A2))) <=> ![P: $i, A1: $i, A2: $i] : ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | ?[Z: $i] : (iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P) & iext(uri_owl_targetIndividual, Z, A2)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(225,plain,
% 1.24/1.40 (^[P: $i, A1: $i, A2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((ir(A1) & ip(P)) & ir(A2)) <=> (ir(A1) & ip(P) & ir(A2))), ((((ir(A1) & ip(P)) & ir(A2)) & (~iext(P, A1, A2))) <=> ((ir(A1) & ip(P) & ir(A2)) & (~iext(P, A1, A2))))), rewrite(((ir(A1) & ip(P) & ir(A2)) & (~iext(P, A1, A2))) <=> (ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))), ((((ir(A1) & ip(P)) & ir(A2)) & (~iext(P, A1, A2))) <=> (ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2))))), quant_intro(proof_bind(^[Z: $i] : rewrite(((iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P)) & iext(uri_owl_targetIndividual, Z, A2)) <=> (iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P) & iext(uri_owl_targetIndividual, Z, A2)))), (?[Z: $i] : ((iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P)) & iext(uri_owl_targetIndividual, Z, A2)) <=> ?[Z: $i] : (iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P) & iext(uri_owl_targetIndividual, Z, A2)))), (((((ir(A1) & ip(P)) & ir(A2)) & (~iext(P, A1, A2))) => ?[Z: $i] : ((iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P)) & iext(uri_owl_targetIndividual, Z, A2))) <=> ((ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2))) => ?[Z: $i] : (iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P) & iext(uri_owl_targetIndividual, Z, A2))))), rewrite(((ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2))) => ?[Z: $i] : (iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P) & iext(uri_owl_targetIndividual, Z, A2))) <=> ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | ?[Z: $i] : (iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P) & iext(uri_owl_targetIndividual, Z, A2)))), (((((ir(A1) & ip(P)) & ir(A2)) & (~iext(P, A1, A2))) => ?[Z: $i] : ((iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P)) & iext(uri_owl_targetIndividual, Z, A2))) <=> ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | ?[Z: $i] : (iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P) & iext(uri_owl_targetIndividual, Z, A2)))))),
% 1.24/1.40 inference(bind,[status(th)],[])).
% 1.24/1.40 tff(226,plain,
% 1.24/1.40 (![P: $i, A1: $i, A2: $i] : ((((ir(A1) & ip(P)) & ir(A2)) & (~iext(P, A1, A2))) => ?[Z: $i] : ((iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P)) & iext(uri_owl_targetIndividual, Z, A2))) <=> ![P: $i, A1: $i, A2: $i] : ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | ?[Z: $i] : (iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P) & iext(uri_owl_targetIndividual, Z, A2)))),
% 1.24/1.40 inference(quant_intro,[status(thm)],[225])).
% 1.24/1.40 tff(227,axiom,(![P: $i, A1: $i, A2: $i] : ((((ir(A1) & ip(P)) & ir(A2)) & (~iext(P, A1, A2))) => ?[Z: $i] : ((iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P)) & iext(uri_owl_targetIndividual, Z, A2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','owl_npa_object_fi')).
% 1.24/1.40 tff(228,plain,
% 1.24/1.40 (![P: $i, A1: $i, A2: $i] : ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | ?[Z: $i] : (iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P) & iext(uri_owl_targetIndividual, Z, A2)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.24/1.40 tff(229,plain,
% 1.24/1.40 (![P: $i, A1: $i, A2: $i] : ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | ?[Z: $i] : (iext(uri_owl_sourceIndividual, Z, A1) & iext(uri_owl_assertionProperty, Z, P) & iext(uri_owl_targetIndividual, Z, A2)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[228, 224])).
% 1.24/1.40 tff(230,plain,(
% 1.24/1.40 ![P: $i, A1: $i, A2: $i] : ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | (iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1) & iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P) & iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))),
% 1.24/1.40 inference(skolemize,[status(sab)],[229])).
% 1.24/1.40 tff(231,plain,
% 1.24/1.40 (![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[230, 223])).
% 1.24/1.40 tff(232,plain,
% 1.24/1.40 (![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[231, 221])).
% 1.24/1.40 tff(233,plain,
% 1.24/1.40 (((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))) | ((~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)))) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o)))) <=> ((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))) | (~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)))) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(234,plain,
% 1.24/1.40 ((iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o)) | (~ir(uri_ex_s)) | (~ip(uri_ex_p)) | (~((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p))))) <=> ((~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)))) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(235,plain,
% 1.24/1.40 ((~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)))) <=> (~((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(236,plain,
% 1.24/1.40 ((iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o)) | (~ir(uri_ex_s)) | (~ip(uri_ex_p)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o))))) <=> (iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o)) | (~ir(uri_ex_s)) | (~ip(uri_ex_p)) | (~((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[235])).
% 1.24/1.40 tff(237,plain,
% 1.24/1.40 ((iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o)) | (~ir(uri_ex_s)) | (~ip(uri_ex_p)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o))))) <=> ((~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)))) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[236, 234])).
% 1.24/1.40 tff(238,plain,
% 1.24/1.40 (((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))) | (iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o)) | (~ir(uri_ex_s)) | (~ip(uri_ex_p)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)))))) <=> ((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))) | ((~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)))) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[237])).
% 1.24/1.40 tff(239,plain,
% 1.24/1.40 (((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))) | (iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o)) | (~ir(uri_ex_s)) | (~ip(uri_ex_p)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)))))) <=> ((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))) | (~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)))) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[238, 233])).
% 1.24/1.40 tff(240,plain,
% 1.24/1.40 ((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))) | (iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o)) | (~ir(uri_ex_s)) | (~ip(uri_ex_p)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(241,plain,
% 1.24/1.40 ((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ir(A2)) | (~ir(A1)) | (~ip(P)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_2(A2, A1, P), A2)))))) | (~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~((~iext(uri_owl_targetIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_2(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)))) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ir(uri_ex_o))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[240, 239])).
% 1.24/1.40 tff(242,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[241, 232, 219, 200, 196, 185, 127])).
% 1.24/1.40 % SZS output end Proof
% 1.24/1.40 % E exiting
%------------------------------------------------------------------------------