TSTP Solution File: SWB010+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB010+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 : Tue Sep 20 08:31:40 EDT 2022
% Result : Theorem 95.69s 61.57s
% Output : Proof 95.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWB010+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 19:20:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 95.69/61.57 % SZS status Theorem
% 95.69/61.57 % SZS output start Proof
% 95.69/61.57 tff(icext_type, type, (
% 95.69/61.57 icext: ( $i * $i ) > $o)).
% 95.69/61.57 tff(uri_ex_o_type, type, (
% 95.69/61.57 uri_ex_o: $i)).
% 95.69/61.57 tff(tptp_fun_BNODE_x3_141_type, type, (
% 95.69/61.57 tptp_fun_BNODE_x3_141: $i)).
% 95.69/61.57 tff(tptp_fun_BNODE_x2_142_type, type, (
% 95.69/61.57 tptp_fun_BNODE_x2_142: $i)).
% 95.69/61.57 tff(ic_type, type, (
% 95.69/61.57 ic: $i > $o)).
% 95.69/61.57 tff(iext_type, type, (
% 95.69/61.57 iext: ( $i * $i * $i ) > $o)).
% 95.69/61.57 tff(uri_owl_complementOf_type, type, (
% 95.69/61.57 uri_owl_complementOf: $i)).
% 95.69/61.57 tff(uri_rdf_nil_type, type, (
% 95.69/61.57 uri_rdf_nil: $i)).
% 95.69/61.57 tff(tptp_fun_BNODE_x4_140_type, type, (
% 95.69/61.57 tptp_fun_BNODE_x4_140: $i)).
% 95.69/61.57 tff(uri_rdf_rest_type, type, (
% 95.69/61.57 uri_rdf_rest: $i)).
% 95.69/61.57 tff(uri_rdf_first_type, type, (
% 95.69/61.57 uri_rdf_first: $i)).
% 95.69/61.57 tff(uri_owl_oneOf_type, type, (
% 95.69/61.57 uri_owl_oneOf: $i)).
% 95.69/61.57 tff(tptp_fun_BNODE_x1_143_type, type, (
% 95.69/61.57 tptp_fun_BNODE_x1_143: $i)).
% 95.69/61.57 tff(uri_owl_allValuesFrom_type, type, (
% 95.69/61.57 uri_owl_allValuesFrom: $i)).
% 95.69/61.57 tff(uri_ex_p_type, type, (
% 95.69/61.57 uri_ex_p: $i)).
% 95.69/61.57 tff(uri_owl_onProperty_type, type, (
% 95.69/61.57 uri_owl_onProperty: $i)).
% 95.69/61.57 tff(uri_ex_s_type, type, (
% 95.69/61.57 uri_ex_s: $i)).
% 95.69/61.57 tff(uri_rdf_type_type, type, (
% 95.69/61.57 uri_rdf_type: $i)).
% 95.69/61.57 tff(uri_owl_ObjectProperty_type, type, (
% 95.69/61.57 uri_owl_ObjectProperty: $i)).
% 95.69/61.57 tff(tptp_fun_Z_139_type, type, (
% 95.69/61.57 tptp_fun_Z_139: ( $i * $i * $i ) > $i)).
% 95.69/61.57 tff(uri_owl_sourceIndividual_type, type, (
% 95.69/61.57 uri_owl_sourceIndividual: $i)).
% 95.69/61.57 tff(uri_owl_targetIndividual_type, type, (
% 95.69/61.57 uri_owl_targetIndividual: $i)).
% 95.69/61.57 tff(uri_owl_assertionProperty_type, type, (
% 95.69/61.57 uri_owl_assertionProperty: $i)).
% 95.69/61.57 tff(uri_owl_NegativePropertyAssertion_type, type, (
% 95.69/61.57 uri_owl_NegativePropertyAssertion: $i)).
% 95.69/61.57 tff(ir_type, type, (
% 95.69/61.57 ir: $i > $o)).
% 95.69/61.57 tff(uri_rdfs_Resource_type, type, (
% 95.69/61.57 uri_rdfs_Resource: $i)).
% 95.69/61.57 tff(ip_type, type, (
% 95.69/61.57 ip: $i > $o)).
% 95.69/61.57 tff(uri_rdfs_range_type, type, (
% 95.69/61.57 uri_rdfs_range: $i)).
% 95.69/61.57 tff(tptp_fun_Y_59_type, type, (
% 95.69/61.57 tptp_fun_Y_59: ( $i * $i ) > $i)).
% 95.69/61.57 tff(tptp_fun_X_60_type, type, (
% 95.69/61.57 tptp_fun_X_60: ( $i * $i ) > $i)).
% 95.69/61.57 tff(uri_rdfs_domain_type, type, (
% 95.69/61.57 uri_rdfs_domain: $i)).
% 95.69/61.57 tff(tptp_fun_X_58_type, type, (
% 95.69/61.57 tptp_fun_X_58: ( $i * $i ) > $i)).
% 95.69/61.57 tff(tptp_fun_Y_57_type, type, (
% 95.69/61.57 tptp_fun_Y_57: ( $i * $i ) > $i)).
% 95.69/61.57 tff(uri_owl_Restriction_type, type, (
% 95.69/61.57 uri_owl_Restriction: $i)).
% 95.69/61.57 tff(tptp_fun_Y_11_type, type, (
% 95.69/61.57 tptp_fun_Y_11: ( $i * $i * $i ) > $i)).
% 95.69/61.57 tff(tptp_fun_X_8_type, type, (
% 95.69/61.57 tptp_fun_X_8: ( $i * $i ) > $i)).
% 95.69/61.57 tff(1,plain,
% 95.69/61.57 (?[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))),
% 95.69/61.57 inference(rewrite,[status(thm)],[])).
% 95.69/61.57 tff(2,plain,
% 95.69/61.57 (^[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))))),
% 95.69/61.57 inference(bind,[status(th)],[])).
% 95.69/61.57 tff(3,plain,
% 95.69/61.57 (?[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))),
% 95.69/61.57 inference(quant_intro,[status(thm)],[2])).
% 95.69/61.57 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')).
% 95.69/61.57 tff(5,plain,
% 95.69/61.57 (?[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))),
% 95.69/61.57 inference(modus_ponens,[status(thm)],[4, 3])).
% 95.69/61.57 tff(6,plain,
% 95.69/61.57 (?[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))),
% 95.69/61.57 inference(modus_ponens,[status(thm)],[5, 1])).
% 95.69/61.57 tff(7,plain,(
% 95.69/61.57 iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) & iext(uri_rdf_type, uri_ex_s, BNODE_x1!143) & iext(uri_owl_onProperty, BNODE_x1!143, uri_ex_p) & iext(uri_owl_allValuesFrom, BNODE_x1!143, BNODE_x2!142) & iext(uri_owl_complementOf, BNODE_x2!142, BNODE_x3!141) & iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140) & iext(uri_rdf_first, BNODE_x4!140, uri_ex_o) & iext(uri_rdf_rest, BNODE_x4!140, uri_rdf_nil)),
% 95.69/61.57 inference(skolemize,[status(sab)],[6])).
% 95.69/61.57 tff(8,plain,
% 95.69/61.57 (iext(uri_owl_complementOf, BNODE_x2!142, BNODE_x3!141)),
% 95.69/61.57 inference(and_elim,[status(thm)],[7])).
% 95.69/61.57 tff(9,plain,
% 95.69/61.57 (^[Z: $i, C: $i] : refl(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))))),
% 95.69/61.57 inference(bind,[status(th)],[])).
% 95.69/61.57 tff(10,plain,
% 95.69/61.57 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 95.69/61.57 inference(quant_intro,[status(thm)],[9])).
% 95.69/61.57 tff(11,plain,
% 95.69/61.57 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))))),
% 95.69/61.57 inference(bind,[status(th)],[])).
% 95.69/61.57 tff(12,plain,
% 95.69/61.57 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 95.69/61.57 inference(quant_intro,[status(thm)],[11])).
% 95.69/61.57 tff(13,plain,
% 95.69/61.57 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 95.69/61.57 inference(transitivity,[status(thm)],[12, 10])).
% 95.69/61.57 tff(14,plain,
% 95.69/61.57 (^[Z: $i, C: $i] : rewrite(((~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(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))))),
% 95.69/61.57 inference(bind,[status(th)],[])).
% 95.69/61.57 tff(15,plain,
% 95.69/61.57 (![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(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 95.69/61.57 inference(quant_intro,[status(thm)],[14])).
% 95.69/61.57 tff(16,plain,
% 95.69/61.57 (![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(Z, X) <=> (~icext(C, X)))))),
% 95.69/61.57 inference(rewrite,[status(thm)],[])).
% 95.69/61.57 tff(17,plain,
% 95.69/61.57 (^[Z: $i, C: $i] : trans(monotonicity(rewrite(((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))) <=> (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(Z, X) <=> (~icext(C, X))))) <=> (iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))), rewrite((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(Z, X) <=> (~icext(C, 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(Z, X) <=> (~icext(C, X)))))))),
% 95.69/61.57 inference(bind,[status(th)],[])).
% 95.69/61.57 tff(18,plain,
% 95.69/61.57 (![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(Z, X) <=> (~icext(C, X)))))),
% 95.69/61.57 inference(quant_intro,[status(thm)],[17])).
% 95.69/61.57 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/Axioms/SWB001+0.ax','owl_bool_complementof_class')).
% 95.69/61.57 tff(20,plain,
% 95.69/61.57 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))),
% 95.69/61.57 inference(modus_ponens,[status(thm)],[19, 18])).
% 95.69/61.57 tff(21,plain,
% 95.69/61.57 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))),
% 95.69/61.57 inference(modus_ponens,[status(thm)],[20, 16])).
% 95.69/61.57 tff(22,plain,(
% 95.69/61.57 ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))),
% 95.69/61.57 inference(skolemize,[status(sab)],[21])).
% 95.69/61.57 tff(23,plain,
% 95.69/61.57 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 95.69/61.57 inference(modus_ponens,[status(thm)],[22, 15])).
% 95.69/61.57 tff(24,plain,
% 95.69/61.57 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 95.69/61.57 inference(modus_ponens,[status(thm)],[23, 13])).
% 95.69/61.57 tff(25,plain,
% 95.69/61.57 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, BNODE_x2!142, BNODE_x3!141)) | (~((~ic(BNODE_x2!142)) | (~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | (~iext(uri_owl_complementOf, BNODE_x2!142, BNODE_x3!141)) | (~((~ic(BNODE_x2!142)) | (~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X)))))))),
% 95.69/61.57 inference(rewrite,[status(thm)],[])).
% 95.69/61.57 tff(26,plain,
% 95.69/61.57 (((~iext(uri_owl_complementOf, BNODE_x2!142, BNODE_x3!141)) | (~((~ic(BNODE_x3!141)) | (~ic(BNODE_x2!142)) | (~![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X))))))) <=> ((~iext(uri_owl_complementOf, BNODE_x2!142, BNODE_x3!141)) | (~((~ic(BNODE_x2!142)) | (~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X)))))))),
% 95.69/61.57 inference(rewrite,[status(thm)],[])).
% 95.69/61.57 tff(27,plain,
% 95.69/61.57 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, BNODE_x2!142, BNODE_x3!141)) | (~((~ic(BNODE_x3!141)) | (~ic(BNODE_x2!142)) | (~![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, BNODE_x2!142, BNODE_x3!141)) | (~((~ic(BNODE_x2!142)) | (~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X))))))))),
% 95.69/61.57 inference(monotonicity,[status(thm)],[26])).
% 95.69/61.57 tff(28,plain,
% 95.69/61.57 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, BNODE_x2!142, BNODE_x3!141)) | (~((~ic(BNODE_x3!141)) | (~ic(BNODE_x2!142)) | (~![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | (~iext(uri_owl_complementOf, BNODE_x2!142, BNODE_x3!141)) | (~((~ic(BNODE_x2!142)) | (~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X)))))))),
% 95.69/61.57 inference(transitivity,[status(thm)],[27, 25])).
% 95.69/61.57 tff(29,plain,
% 95.69/61.57 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, BNODE_x2!142, BNODE_x3!141)) | (~((~ic(BNODE_x3!141)) | (~ic(BNODE_x2!142)) | (~![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X)))))))),
% 95.69/61.57 inference(quant_inst,[status(thm)],[])).
% 95.69/61.57 tff(30,plain,
% 95.69/61.57 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | (~iext(uri_owl_complementOf, BNODE_x2!142, BNODE_x3!141)) | (~((~ic(BNODE_x2!142)) | (~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X))))))),
% 95.69/61.57 inference(modus_ponens,[status(thm)],[29, 28])).
% 95.69/61.57 tff(31,plain,
% 95.69/61.57 (~((~ic(BNODE_x2!142)) | (~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X)))))),
% 95.69/61.57 inference(unit_resolution,[status(thm)],[30, 24, 8])).
% 95.69/61.57 tff(32,plain,
% 95.69/61.57 (((~ic(BNODE_x2!142)) | (~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X))))) | ![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X)))),
% 95.69/61.57 inference(tautology,[status(thm)],[])).
% 95.69/61.57 tff(33,plain,
% 95.69/61.57 (![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X)))),
% 95.69/61.57 inference(unit_resolution,[status(thm)],[32, 31])).
% 95.69/61.57 tff(34,plain,
% 95.69/61.57 ((~![X: $i] : (icext(BNODE_x2!142, X) <=> (~icext(BNODE_x3!141, X)))) | (icext(BNODE_x2!142, uri_ex_o) <=> (~icext(BNODE_x3!141, uri_ex_o)))),
% 95.69/61.57 inference(quant_inst,[status(thm)],[])).
% 95.69/61.57 tff(35,plain,
% 95.69/61.57 (icext(BNODE_x2!142, uri_ex_o) <=> (~icext(BNODE_x3!141, uri_ex_o))),
% 95.69/61.57 inference(unit_resolution,[status(thm)],[34, 33])).
% 95.69/61.57 tff(36,assumption,(~iext(uri_ex_p, uri_ex_s, uri_ex_o)), introduced(assumption)).
% 95.69/61.57 tff(37,assumption,(~((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)))), introduced(assumption)).
% 95.69/61.57 tff(38,plain,
% 95.69/61.57 (((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s))) | iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)),
% 95.69/61.58 inference(tautology,[status(thm)],[])).
% 95.69/61.58 tff(39,plain,
% 95.69/61.58 (iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)),
% 95.69/61.58 inference(unit_resolution,[status(thm)],[38, 37])).
% 95.69/61.58 tff(40,plain,
% 95.69/61.58 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~ir(Y)) | (~icext(uri_owl_NegativePropertyAssertion, X))))) <=> ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~ir(Y)) | (~icext(uri_owl_NegativePropertyAssertion, X))))))),
% 95.69/61.58 inference(bind,[status(th)],[])).
% 95.69/61.58 tff(41,plain,
% 95.69/61.58 (![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~ir(Y)) | (~icext(uri_owl_NegativePropertyAssertion, X))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~ir(Y)) | (~icext(uri_owl_NegativePropertyAssertion, X)))))),
% 95.69/61.58 inference(quant_intro,[status(thm)],[40])).
% 95.69/61.58 tff(42,plain,
% 95.69/61.58 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_sourceIndividual, X, Y)) | (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y))) <=> ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~ir(Y)) | (~icext(uri_owl_NegativePropertyAssertion, X))))))),
% 95.69/61.58 inference(bind,[status(th)],[])).
% 95.69/61.58 tff(43,plain,
% 95.69/61.58 (![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)) | (~((~ir(Y)) | (~icext(uri_owl_NegativePropertyAssertion, X)))))),
% 95.69/61.58 inference(quant_intro,[status(thm)],[42])).
% 95.69/61.58 tff(44,plain,
% 95.69/61.58 (![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)))),
% 95.69/61.58 inference(rewrite,[status(thm)],[])).
% 95.69/61.58 tff(45,plain,
% 95.69/61.58 (^[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))))),
% 95.69/61.58 inference(bind,[status(th)],[])).
% 95.69/61.58 tff(46,plain,
% 95.69/61.58 (![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)))),
% 95.69/61.58 inference(quant_intro,[status(thm)],[45])).
% 95.69/61.58 tff(47,axiom,(![X: $i, Y: $i] : (iext(uri_owl_sourceIndividual, X, Y) => (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_prop_sourceindividual_ext')).
% 95.69/61.58 tff(48,plain,
% 95.69/61.58 (![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y)))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[47, 46])).
% 95.69/61.58 tff(49,plain,
% 95.69/61.58 (![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y)))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[48, 44])).
% 95.69/61.58 tff(50,plain,(
% 95.69/61.58 ![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (icext(uri_owl_NegativePropertyAssertion, X) & ir(Y)))),
% 95.69/61.58 inference(skolemize,[status(sab)],[49])).
% 95.69/61.58 tff(51,plain,
% 95.69/61.58 (![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~ir(Y)) | (~icext(uri_owl_NegativePropertyAssertion, X)))))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[50, 43])).
% 95.69/61.58 tff(52,plain,
% 95.69/61.58 (![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~ir(Y)) | (~icext(uri_owl_NegativePropertyAssertion, X)))))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[51, 41])).
% 95.69/61.58 tff(53,plain,
% 95.69/61.58 (((~![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~ir(Y)) | (~icext(uri_owl_NegativePropertyAssertion, X)))))) | ((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p))))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~ir(Y)) | (~icext(uri_owl_NegativePropertyAssertion, X)))))) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p))))))),
% 95.69/61.58 inference(rewrite,[status(thm)],[])).
% 95.69/61.58 tff(54,plain,
% 95.69/61.58 ((~![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~ir(Y)) | (~icext(uri_owl_NegativePropertyAssertion, X)))))) | ((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p))))))),
% 95.69/61.58 inference(quant_inst,[status(thm)],[])).
% 95.69/61.58 tff(55,plain,
% 95.69/61.58 ((~![X: $i, Y: $i] : ((~iext(uri_owl_sourceIndividual, X, Y)) | (~((~ir(Y)) | (~icext(uri_owl_NegativePropertyAssertion, X)))))) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p)))))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[54, 53])).
% 95.69/61.58 tff(56,plain,
% 95.69/61.58 (~((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p))))),
% 95.69/61.58 inference(unit_resolution,[status(thm)],[55, 52, 39])).
% 95.69/61.58 tff(57,plain,
% 95.69/61.58 (((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s))) | iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)),
% 95.69/61.58 inference(tautology,[status(thm)],[])).
% 95.69/61.58 tff(58,plain,
% 95.69/61.58 (iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)),
% 95.69/61.58 inference(unit_resolution,[status(thm)],[57, 37])).
% 95.69/61.58 tff(59,plain,
% 95.69/61.58 (((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s))) | iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)),
% 95.69/61.58 inference(tautology,[status(thm)],[])).
% 95.69/61.58 tff(60,plain,
% 95.69/61.58 (iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)),
% 95.69/61.58 inference(unit_resolution,[status(thm)],[59, 37])).
% 95.69/61.58 tff(61,plain,
% 95.69/61.58 (^[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))))),
% 95.69/61.58 inference(bind,[status(th)],[])).
% 95.69/61.58 tff(62,plain,
% 95.69/61.58 (![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)))),
% 95.69/61.58 inference(quant_intro,[status(thm)],[61])).
% 95.69/61.58 tff(63,plain,
% 95.69/61.58 (^[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)))))),
% 95.69/61.58 inference(bind,[status(th)],[])).
% 95.69/61.58 tff(64,plain,
% 95.69/61.58 (![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)))),
% 95.69/61.58 inference(quant_intro,[status(thm)],[63])).
% 95.69/61.58 tff(65,plain,
% 95.69/61.58 ((~?[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)))),
% 95.69/61.58 inference(rewrite,[status(thm)],[])).
% 95.69/61.58 tff(66,plain,
% 95.69/61.58 ((~?[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)))),
% 95.69/61.58 inference(rewrite,[status(thm)],[])).
% 95.69/61.58 tff(67,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')).
% 95.69/61.58 tff(68,plain,
% 95.69/61.58 (~?[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))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[67, 66])).
% 95.69/61.58 tff(69,plain,
% 95.69/61.58 (~?[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))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[68, 65])).
% 95.69/61.58 tff(70,plain,
% 95.69/61.58 (~?[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))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[69, 65])).
% 95.69/61.58 tff(71,plain,
% 95.69/61.58 (~?[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))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[70, 65])).
% 95.69/61.58 tff(72,plain,
% 95.69/61.58 (~?[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))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[71, 65])).
% 95.69/61.58 tff(73,plain,
% 95.69/61.58 (~?[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))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[72, 65])).
% 95.69/61.58 tff(74,plain,
% 95.69/61.58 (~?[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))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[73, 65])).
% 95.69/61.58 tff(75,plain,
% 95.69/61.58 (^[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)))))),
% 95.69/61.58 inference(bind,[status(th)],[])).
% 95.69/61.58 tff(76,plain,(
% 95.69/61.58 ![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)))),
% 95.69/61.58 inference(nnf-neg,[status(sab)],[74, 75])).
% 95.69/61.58 tff(77,plain,
% 95.69/61.58 (![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)))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[76, 64])).
% 95.69/61.58 tff(78,plain,
% 95.69/61.58 (![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)))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[77, 62])).
% 95.69/61.58 tff(79,plain,
% 95.69/61.58 (((~![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_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_rdf_type, tptp_fun_Z_139(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_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_rdf_type, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)))),
% 95.69/61.58 inference(rewrite,[status(thm)],[])).
% 95.69/61.58 tff(80,plain,
% 95.69/61.58 (((~iext(uri_rdf_type, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o))) <=> ((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_rdf_type, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)))),
% 95.69/61.58 inference(rewrite,[status(thm)],[])).
% 95.69/61.58 tff(81,plain,
% 95.69/61.58 (((~![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_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(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_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_rdf_type, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion))))),
% 95.69/61.58 inference(monotonicity,[status(thm)],[80])).
% 95.69/61.58 tff(82,plain,
% 95.69/61.58 (((~![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_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(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_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_rdf_type, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)))),
% 95.69/61.58 inference(transitivity,[status(thm)],[81, 79])).
% 95.69/61.58 tff(83,plain,
% 95.69/61.58 ((~![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_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)))),
% 95.69/61.58 inference(quant_inst,[status(thm)],[])).
% 95.69/61.58 tff(84,plain,
% 95.69/61.58 ((~![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_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_rdf_type, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[83, 82])).
% 95.69/61.58 tff(85,plain,
% 95.69/61.58 (~iext(uri_rdf_type, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion)),
% 95.69/61.58 inference(unit_resolution,[status(thm)],[84, 78, 60, 58, 39])).
% 95.69/61.58 tff(86,assumption,(~(iext(uri_rdf_type, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion) <=> icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p)))), introduced(assumption)).
% 95.69/61.58 tff(87,plain,
% 95.69/61.58 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 95.69/61.58 inference(bind,[status(th)],[])).
% 95.69/61.58 tff(88,plain,
% 95.69/61.58 (![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))),
% 95.69/61.58 inference(quant_intro,[status(thm)],[87])).
% 95.69/61.58 tff(89,plain,
% 95.69/61.58 (![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))),
% 95.69/61.58 inference(rewrite,[status(thm)],[])).
% 95.69/61.58 tff(90,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','rdfs_cext_def')).
% 95.69/61.58 tff(91,plain,
% 95.69/61.58 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[90, 89])).
% 95.69/61.58 tff(92,plain,(
% 95.69/61.58 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 95.69/61.58 inference(skolemize,[status(sab)],[91])).
% 95.69/61.58 tff(93,plain,
% 95.69/61.58 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[92, 88])).
% 95.69/61.58 tff(94,plain,
% 95.69/61.58 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion) <=> icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p)))),
% 95.69/61.58 inference(quant_inst,[status(thm)],[])).
% 95.69/61.58 tff(95,plain,
% 95.69/61.58 ($false),
% 95.69/61.58 inference(unit_resolution,[status(thm)],[94, 93, 86])).
% 95.69/61.58 tff(96,plain,(iext(uri_rdf_type, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion) <=> icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p))), inference(lemma,lemma(discharge,[]))).
% 95.69/61.58 tff(97,plain,
% 95.69/61.58 ((~(iext(uri_rdf_type, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion) <=> icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p)))) | iext(uri_rdf_type, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p)))),
% 95.69/61.58 inference(tautology,[status(thm)],[])).
% 95.69/61.58 tff(98,plain,
% 95.69/61.58 (iext(uri_rdf_type, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_owl_NegativePropertyAssertion) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p)))),
% 95.69/61.58 inference(unit_resolution,[status(thm)],[97, 96])).
% 95.69/61.58 tff(99,plain,
% 95.69/61.58 (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p))),
% 95.69/61.58 inference(unit_resolution,[status(thm)],[98, 85])).
% 95.69/61.58 tff(100,plain,
% 95.69/61.58 (((~ir(uri_ex_s)) | (~icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p)))) | icext(uri_owl_NegativePropertyAssertion, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p))),
% 95.69/61.58 inference(tautology,[status(thm)],[])).
% 95.69/61.58 tff(101,plain,
% 95.69/61.58 ($false),
% 95.69/61.58 inference(unit_resolution,[status(thm)],[100, 99, 56])).
% 95.69/61.58 tff(102,plain,((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s))), inference(lemma,lemma(discharge,[]))).
% 95.69/61.58 tff(103,plain,
% 95.69/61.58 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))))))),
% 95.69/61.58 inference(bind,[status(th)],[])).
% 95.69/61.58 tff(104,plain,
% 95.69/61.58 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> ![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))),
% 95.69/61.58 inference(quant_intro,[status(thm)],[103])).
% 95.69/61.58 tff(105,plain,
% 95.69/61.58 (^[P: $i, C: $i] : refl((~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))))),
% 95.69/61.58 inference(bind,[status(th)],[])).
% 95.69/61.58 tff(106,plain,
% 95.69/61.58 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 95.69/61.58 inference(quant_intro,[status(thm)],[105])).
% 95.69/61.58 tff(107,plain,
% 95.69/61.58 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))))),
% 95.69/61.58 inference(bind,[status(th)],[])).
% 95.69/61.58 tff(108,plain,
% 95.69/61.58 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 95.69/61.58 inference(quant_intro,[status(thm)],[107])).
% 95.69/61.58 tff(109,plain,
% 95.69/61.58 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 95.69/61.58 inference(transitivity,[status(thm)],[108, 106])).
% 95.69/61.58 tff(110,plain,
% 95.69/61.58 (^[P: $i, C: $i] : trans(monotonicity(rewrite(((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) <=> ((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))), rewrite((iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))) <=> (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))), ((((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) <=> (((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))), rewrite((((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) <=> (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))), ((((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) <=> (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))))),
% 95.69/61.58 inference(bind,[status(th)],[])).
% 95.69/61.58 tff(111,plain,
% 95.69/61.58 (![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 95.69/61.58 inference(quant_intro,[status(thm)],[110])).
% 95.69/61.58 tff(112,plain,
% 95.69/61.58 (^[P: $i, C: $i] : rewrite((((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | ((~ip(P)) | (~ip(C)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))) <=> (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))),
% 95.69/61.58 inference(bind,[status(th)],[])).
% 95.69/61.58 tff(113,plain,
% 95.69/61.58 (![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | ((~ip(P)) | (~ip(C)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))) <=> ![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))),
% 95.69/61.58 inference(quant_intro,[status(thm)],[112])).
% 95.69/61.58 tff(114,plain,
% 95.69/61.58 (![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 95.69/61.58 inference(rewrite,[status(thm)],[])).
% 95.69/61.58 tff(115,plain,
% 95.69/61.58 (^[P: $i, C: $i] : rewrite((iext(uri_rdfs_range, P, C) <=> ((ip(P) & ip(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, Y)))) <=> (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))),
% 95.69/61.58 inference(bind,[status(th)],[])).
% 95.69/61.58 tff(116,plain,
% 95.69/61.58 (![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> ((ip(P) & ip(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, Y)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 95.69/61.58 inference(quant_intro,[status(thm)],[115])).
% 95.69/61.58 tff(117,axiom,(![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> ((ip(P) & ip(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_rdfsext_range')).
% 95.69/61.58 tff(118,plain,
% 95.69/61.58 (![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[117, 116])).
% 95.69/61.58 tff(119,plain,
% 95.69/61.58 (![P: $i, C: $i] : (iext(uri_rdfs_range, P, C) <=> (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))),
% 95.69/61.58 inference(modus_ponens,[status(thm)],[118, 114])).
% 95.69/61.58 tff(120,plain,(
% 95.69/61.58 ![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | ((~ip(P)) | (~ip(C)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))))),
% 95.69/61.59 inference(skolemize,[status(sab)],[119])).
% 95.69/61.59 tff(121,plain,
% 95.69/61.59 (![P: $i, C: $i] : (((~iext(uri_rdfs_range, P, C)) | (ip(P) & ip(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) & (iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))),
% 95.69/61.59 inference(modus_ponens,[status(thm)],[120, 113])).
% 95.69/61.59 tff(122,plain,
% 95.69/61.59 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 95.69/61.59 inference(modus_ponens,[status(thm)],[121, 111])).
% 95.69/61.59 tff(123,plain,
% 95.69/61.59 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))))))) | (~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P))))))))),
% 95.69/61.59 inference(modus_ponens,[status(thm)],[122, 109])).
% 95.69/61.59 tff(124,plain,
% 95.69/61.59 (![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))),
% 95.69/61.59 inference(modus_ponens,[status(thm)],[123, 104])).
% 95.69/61.59 tff(125,plain,
% 95.69/61.59 (((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource) | (~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~((~iext(uri_rdf_first, tptp_fun_X_60(uri_rdfs_Resource, uri_rdf_first), tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first))) | icext(uri_rdfs_Resource, tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first)))))) | (~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y)))))))))) <=> ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource) | (~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~((~iext(uri_rdf_first, tptp_fun_X_60(uri_rdfs_Resource, uri_rdf_first), tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first))) | icext(uri_rdfs_Resource, tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first)))))) | (~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))))))))))),
% 95.69/61.59 inference(rewrite,[status(thm)],[])).
% 95.69/61.59 tff(126,plain,
% 95.69/61.59 ((~((~(iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource) | (~ip(uri_rdfs_Resource)) | (~ip(uri_rdf_first)) | (~((~iext(uri_rdf_first, tptp_fun_X_60(uri_rdfs_Resource, uri_rdf_first), tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first))) | icext(uri_rdfs_Resource, tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first)))))) | (~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdfs_Resource)) | (~ip(uri_rdf_first)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))))))))) <=> (~((~(iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource) | (~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~((~iext(uri_rdf_first, tptp_fun_X_60(uri_rdfs_Resource, uri_rdf_first), tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first))) | icext(uri_rdfs_Resource, tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first)))))) | (~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y)))))))))),
% 95.69/61.59 inference(rewrite,[status(thm)],[])).
% 95.69/61.59 tff(127,plain,
% 95.69/61.59 (((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource) | (~ip(uri_rdfs_Resource)) | (~ip(uri_rdf_first)) | (~((~iext(uri_rdf_first, tptp_fun_X_60(uri_rdfs_Resource, uri_rdf_first), tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first))) | icext(uri_rdfs_Resource, tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first)))))) | (~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdfs_Resource)) | (~ip(uri_rdf_first)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y)))))))))) <=> ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource) | (~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~((~iext(uri_rdf_first, tptp_fun_X_60(uri_rdfs_Resource, uri_rdf_first), tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first))) | icext(uri_rdfs_Resource, tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first)))))) | (~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))))))))))),
% 95.69/61.59 inference(monotonicity,[status(thm)],[126])).
% 95.69/61.59 tff(128,plain,
% 95.69/61.59 (((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource) | (~ip(uri_rdfs_Resource)) | (~ip(uri_rdf_first)) | (~((~iext(uri_rdf_first, tptp_fun_X_60(uri_rdfs_Resource, uri_rdf_first), tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first))) | icext(uri_rdfs_Resource, tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first)))))) | (~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdfs_Resource)) | (~ip(uri_rdf_first)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y)))))))))) <=> ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource) | (~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~((~iext(uri_rdf_first, tptp_fun_X_60(uri_rdfs_Resource, uri_rdf_first), tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first))) | icext(uri_rdfs_Resource, tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first)))))) | (~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))))))))))),
% 95.69/61.59 inference(transitivity,[status(thm)],[127, 125])).
% 95.69/61.59 tff(129,plain,
% 95.69/61.59 ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource) | (~ip(uri_rdfs_Resource)) | (~ip(uri_rdf_first)) | (~((~iext(uri_rdf_first, tptp_fun_X_60(uri_rdfs_Resource, uri_rdf_first), tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first))) | icext(uri_rdfs_Resource, tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first)))))) | (~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdfs_Resource)) | (~ip(uri_rdf_first)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y)))))))))),
% 95.69/61.59 inference(quant_inst,[status(thm)],[])).
% 95.69/61.59 tff(130,plain,
% 95.69/61.59 ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_range, P, C) | (~ip(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_60(C, P), tptp_fun_Y_59(C, P))) | icext(C, tptp_fun_Y_59(C, P)))))) | (~((~iext(uri_rdfs_range, P, C)) | (~((~ip(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))))))))) | (~((~(iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource) | (~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~((~iext(uri_rdf_first, tptp_fun_X_60(uri_rdfs_Resource, uri_rdf_first), tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first))) | icext(uri_rdfs_Resource, tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first)))))) | (~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y)))))))))),
% 95.69/61.59 inference(modus_ponens,[status(thm)],[129, 128])).
% 95.69/61.59 tff(131,plain,
% 95.69/61.59 (~((~(iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource) | (~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~((~iext(uri_rdf_first, tptp_fun_X_60(uri_rdfs_Resource, uri_rdf_first), tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first))) | icext(uri_rdfs_Resource, tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first)))))) | (~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))))))))),
% 95.69/61.59 inference(unit_resolution,[status(thm)],[130, 124])).
% 95.69/61.59 tff(132,plain,
% 95.69/61.59 (((~(iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource) | (~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~((~iext(uri_rdf_first, tptp_fun_X_60(uri_rdfs_Resource, uri_rdf_first), tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first))) | icext(uri_rdfs_Resource, tptp_fun_Y_59(uri_rdfs_Resource, uri_rdf_first)))))) | (~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y)))))))) | ((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))))))),
% 95.69/61.59 inference(tautology,[status(thm)],[])).
% 95.69/61.59 tff(133,plain,
% 95.69/61.59 ((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y)))))),
% 95.69/61.59 inference(unit_resolution,[status(thm)],[132, 131])).
% 95.69/61.59 tff(134,plain,
% 95.69/61.59 (iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource) <=> iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)),
% 95.69/61.59 inference(rewrite,[status(thm)],[])).
% 95.69/61.59 tff(135,axiom,(iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','rdfs_collection_first_range')).
% 95.69/61.59 tff(136,plain,
% 95.69/61.59 (iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)),
% 95.69/61.59 inference(modus_ponens,[status(thm)],[135, 134])).
% 95.69/61.59 tff(137,plain,
% 95.69/61.59 ((~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))))))) | (~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y)))))),
% 95.69/61.59 inference(tautology,[status(thm)],[])).
% 95.69/61.59 tff(138,plain,
% 95.69/61.59 ((~((~iext(uri_rdfs_range, uri_rdf_first, uri_rdfs_Resource)) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))))))) | (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y)))))),
% 95.69/61.59 inference(unit_resolution,[status(thm)],[137, 136])).
% 95.69/61.59 tff(139,plain,
% 95.69/61.59 (~((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))))),
% 95.69/61.59 inference(unit_resolution,[status(thm)],[138, 133])).
% 95.69/61.59 tff(140,plain,
% 95.69/61.59 (((~ip(uri_rdf_first)) | (~ip(uri_rdfs_Resource)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y)))) | ![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))),
% 95.69/61.59 inference(tautology,[status(thm)],[])).
% 95.69/61.59 tff(141,plain,
% 95.69/61.59 (![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))),
% 95.69/61.59 inference(unit_resolution,[status(thm)],[140, 139])).
% 95.69/61.59 tff(142,plain,
% 95.69/61.59 (iext(uri_rdf_first, BNODE_x4!140, uri_ex_o)),
% 95.69/61.59 inference(and_elim,[status(thm)],[7])).
% 95.69/61.59 tff(143,plain,
% 95.69/61.59 (((~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))) | ((~iext(uri_rdf_first, BNODE_x4!140, uri_ex_o)) | icext(uri_rdfs_Resource, uri_ex_o))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))) | (~iext(uri_rdf_first, BNODE_x4!140, uri_ex_o)) | icext(uri_rdfs_Resource, uri_ex_o))),
% 95.69/61.59 inference(rewrite,[status(thm)],[])).
% 95.69/61.59 tff(144,plain,
% 95.69/61.59 ((~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))) | ((~iext(uri_rdf_first, BNODE_x4!140, uri_ex_o)) | icext(uri_rdfs_Resource, uri_ex_o))),
% 95.69/61.59 inference(quant_inst,[status(thm)],[])).
% 95.69/61.59 tff(145,plain,
% 95.69/61.59 ((~![X: $i, Y: $i] : ((~iext(uri_rdf_first, X, Y)) | icext(uri_rdfs_Resource, Y))) | (~iext(uri_rdf_first, BNODE_x4!140, uri_ex_o)) | icext(uri_rdfs_Resource, uri_ex_o)),
% 95.69/61.59 inference(modus_ponens,[status(thm)],[144, 143])).
% 95.69/61.59 tff(146,plain,
% 95.69/61.59 (icext(uri_rdfs_Resource, uri_ex_o)),
% 95.69/61.59 inference(unit_resolution,[status(thm)],[145, 142, 141])).
% 95.69/61.59 tff(147,plain,
% 95.69/61.59 (ic(uri_rdfs_Resource) <=> ic(uri_rdfs_Resource)),
% 95.69/61.59 inference(rewrite,[status(thm)],[])).
% 95.69/61.59 tff(148,axiom,(ic(uri_rdfs_Resource)), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_class_resource_type')).
% 95.69/61.59 tff(149,plain,
% 95.69/61.59 (ic(uri_rdfs_Resource)),
% 95.69/61.59 inference(modus_ponens,[status(thm)],[148, 147])).
% 95.69/61.59 tff(150,plain,
% 95.69/61.59 (^[X: $i] : refl(((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y)))) <=> ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y)))))),
% 95.69/61.59 inference(bind,[status(th)],[])).
% 95.69/61.59 tff(151,plain,
% 95.69/61.59 (![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y)))) <=> ![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))),
% 95.69/61.59 inference(quant_intro,[status(thm)],[150])).
% 95.69/61.59 tff(152,plain,
% 95.69/61.59 (^[X: $i] : rewrite(((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y)))) <=> ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y)))))),
% 95.69/61.59 inference(bind,[status(th)],[])).
% 95.69/61.59 tff(153,plain,
% 95.69/61.59 (![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y)))) <=> ![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))),
% 95.69/61.59 inference(quant_intro,[status(thm)],[152])).
% 95.69/61.59 tff(154,plain,
% 95.69/61.59 (![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y)))) <=> ![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))),
% 95.69/61.59 inference(transitivity,[status(thm)],[153, 151])).
% 95.69/61.59 tff(155,plain,
% 95.69/61.59 (![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y)))) <=> ![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))),
% 95.69/61.59 inference(rewrite,[status(thm)],[])).
% 95.69/61.59 tff(156,plain,
% 95.69/61.59 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite((icext(X, Y) => ir(Y)) <=> (ir(Y) | (~icext(X, Y))))), (![Y: $i] : (icext(X, Y) => ir(Y)) <=> ![Y: $i] : (ir(Y) | (~icext(X, Y))))), ((ic(X) => ![Y: $i] : (icext(X, Y) => ir(Y))) <=> (ic(X) => ![Y: $i] : (ir(Y) | (~icext(X, Y)))))), rewrite((ic(X) => ![Y: $i] : (ir(Y) | (~icext(X, Y)))) <=> ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))), ((ic(X) => ![Y: $i] : (icext(X, Y) => ir(Y))) <=> ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))))),
% 95.69/61.59 inference(bind,[status(th)],[])).
% 95.69/61.59 tff(157,plain,
% 95.69/61.59 (![X: $i] : (ic(X) => ![Y: $i] : (icext(X, Y) => ir(Y))) <=> ![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))),
% 95.69/61.59 inference(quant_intro,[status(thm)],[156])).
% 95.69/61.59 tff(158,axiom,(![X: $i] : (ic(X) => ![Y: $i] : (icext(X, Y) => ir(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_parts_ic_cond_inst')).
% 95.69/61.59 tff(159,plain,
% 95.69/61.59 (![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))),
% 95.69/61.59 inference(modus_ponens,[status(thm)],[158, 157])).
% 95.69/61.59 tff(160,plain,
% 95.69/61.59 (![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))),
% 95.69/61.59 inference(modus_ponens,[status(thm)],[159, 155])).
% 95.69/61.59 tff(161,plain,(
% 95.69/61.59 ![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))),
% 95.69/61.59 inference(skolemize,[status(sab)],[160])).
% 95.69/61.59 tff(162,plain,
% 95.69/61.59 (![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))),
% 95.69/61.59 inference(modus_ponens,[status(thm)],[161, 154])).
% 95.69/61.59 tff(163,plain,
% 95.69/61.59 (((~![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))) | ((~ic(uri_rdfs_Resource)) | ![Y: $i] : (ir(Y) | (~icext(uri_rdfs_Resource, Y))))) <=> ((~![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))) | (~ic(uri_rdfs_Resource)) | ![Y: $i] : (ir(Y) | (~icext(uri_rdfs_Resource, Y))))),
% 95.69/61.59 inference(rewrite,[status(thm)],[])).
% 95.69/61.59 tff(164,plain,
% 95.69/61.59 ((~![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))) | ((~ic(uri_rdfs_Resource)) | ![Y: $i] : (ir(Y) | (~icext(uri_rdfs_Resource, Y))))),
% 95.69/61.59 inference(quant_inst,[status(thm)],[])).
% 95.69/61.59 tff(165,plain,
% 95.69/61.59 ((~![X: $i] : ((~ic(X)) | ![Y: $i] : (ir(Y) | (~icext(X, Y))))) | (~ic(uri_rdfs_Resource)) | ![Y: $i] : (ir(Y) | (~icext(uri_rdfs_Resource, Y)))),
% 95.69/61.59 inference(modus_ponens,[status(thm)],[164, 163])).
% 95.69/61.59 tff(166,plain,
% 95.69/61.59 (![Y: $i] : (ir(Y) | (~icext(uri_rdfs_Resource, Y)))),
% 95.69/61.59 inference(unit_resolution,[status(thm)],[165, 162, 149])).
% 95.69/61.59 tff(167,plain,
% 95.69/61.59 (((~![Y: $i] : (ir(Y) | (~icext(uri_rdfs_Resource, Y)))) | (ir(uri_ex_o) | (~icext(uri_rdfs_Resource, uri_ex_o)))) <=> ((~![Y: $i] : (ir(Y) | (~icext(uri_rdfs_Resource, Y)))) | ir(uri_ex_o) | (~icext(uri_rdfs_Resource, uri_ex_o)))),
% 95.69/61.59 inference(rewrite,[status(thm)],[])).
% 95.69/61.59 tff(168,plain,
% 95.69/61.59 ((~![Y: $i] : (ir(Y) | (~icext(uri_rdfs_Resource, Y)))) | (ir(uri_ex_o) | (~icext(uri_rdfs_Resource, uri_ex_o)))),
% 95.69/61.59 inference(quant_inst,[status(thm)],[])).
% 95.69/61.59 tff(169,plain,
% 95.69/61.59 ((~![Y: $i] : (ir(Y) | (~icext(uri_rdfs_Resource, Y)))) | ir(uri_ex_o) | (~icext(uri_rdfs_Resource, uri_ex_o))),
% 95.69/61.59 inference(modus_ponens,[status(thm)],[168, 167])).
% 95.69/61.59 tff(170,plain,
% 95.69/61.59 (ir(uri_ex_o)),
% 95.69/61.59 inference(unit_resolution,[status(thm)],[169, 166, 146])).
% 95.69/61.59 tff(171,plain,
% 95.69/61.59 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))))))),
% 95.69/61.59 inference(bind,[status(th)],[])).
% 95.69/61.59 tff(172,plain,
% 95.69/61.59 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))),
% 95.69/61.59 inference(quant_intro,[status(thm)],[171])).
% 95.69/61.59 tff(173,plain,
% 95.69/61.59 (^[P: $i, C: $i] : refl((~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))))),
% 95.69/61.59 inference(bind,[status(th)],[])).
% 95.69/61.59 tff(174,plain,
% 95.69/61.59 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 95.69/61.59 inference(quant_intro,[status(thm)],[173])).
% 95.69/61.59 tff(175,plain,
% 95.69/61.59 (^[P: $i, C: $i] : rewrite((~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))))),
% 95.69/61.59 inference(bind,[status(th)],[])).
% 95.69/61.59 tff(176,plain,
% 95.69/61.59 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 95.69/61.59 inference(quant_intro,[status(thm)],[175])).
% 95.69/61.59 tff(177,plain,
% 95.69/61.59 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 95.69/61.59 inference(transitivity,[status(thm)],[176, 174])).
% 95.69/61.59 tff(178,plain,
% 95.69/61.59 (^[P: $i, C: $i] : trans(monotonicity(rewrite(((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) <=> ((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))), rewrite((iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))) <=> (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))), ((((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> (((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))), rewrite((((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))), ((((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))))),
% 95.69/61.59 inference(bind,[status(th)],[])).
% 95.69/61.59 tff(179,plain,
% 95.69/61.59 (![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) <=> ![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 95.69/61.59 inference(quant_intro,[status(thm)],[178])).
% 95.69/61.59 tff(180,plain,
% 95.69/61.59 (^[P: $i, C: $i] : rewrite((((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | ((~ip(P)) | (~ic(C)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))) <=> (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))),
% 95.69/61.59 inference(bind,[status(th)],[])).
% 95.69/61.59 tff(181,plain,
% 95.69/61.59 (![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | ((~ip(P)) | (~ic(C)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))) <=> ![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))),
% 95.69/61.59 inference(quant_intro,[status(thm)],[180])).
% 95.69/61.59 tff(182,plain,
% 95.69/61.59 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 95.69/61.59 inference(rewrite,[status(thm)],[])).
% 95.69/61.59 tff(183,plain,
% 95.69/61.59 (^[P: $i, C: $i] : rewrite((iext(uri_rdfs_domain, P, C) <=> ((ip(P) & ic(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, X)))) <=> (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))),
% 95.69/61.59 inference(bind,[status(th)],[])).
% 95.69/61.59 tff(184,plain,
% 95.69/61.59 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> ((ip(P) & ic(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, X)))) <=> ![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 95.69/61.59 inference(quant_intro,[status(thm)],[183])).
% 95.69/61.59 tff(185,axiom,(![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> ((ip(P) & ic(C)) & ![X: $i, Y: $i] : (iext(P, X, Y) => icext(C, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_rdfsext_domain')).
% 95.75/61.59 tff(186,plain,
% 95.75/61.59 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 95.75/61.59 inference(modus_ponens,[status(thm)],[185, 184])).
% 95.75/61.59 tff(187,plain,
% 95.75/61.59 (![P: $i, C: $i] : (iext(uri_rdfs_domain, P, C) <=> (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))),
% 95.75/61.59 inference(modus_ponens,[status(thm)],[186, 182])).
% 95.75/61.59 tff(188,plain,(
% 95.75/61.59 ![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | ((~ip(P)) | (~ic(C)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))))),
% 95.75/61.59 inference(skolemize,[status(sab)],[187])).
% 95.75/61.59 tff(189,plain,
% 95.75/61.59 (![P: $i, C: $i] : (((~iext(uri_rdfs_domain, P, C)) | (ip(P) & ic(C) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))) & (iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))),
% 95.75/61.59 inference(modus_ponens,[status(thm)],[188, 181])).
% 95.75/61.59 tff(190,plain,
% 95.75/61.59 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 95.75/61.59 inference(modus_ponens,[status(thm)],[189, 179])).
% 95.75/61.59 tff(191,plain,
% 95.75/61.59 (![P: $i, C: $i] : (~((~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X))))))) | (~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P))))))))),
% 95.75/61.59 inference(modus_ponens,[status(thm)],[190, 177])).
% 95.75/61.59 tff(192,plain,
% 95.75/61.59 (![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))),
% 95.75/61.59 inference(modus_ponens,[status(thm)],[191, 172])).
% 95.75/61.59 tff(193,plain,
% 95.75/61.59 ((~![P: $i, C: $i] : (~((~(iext(uri_rdfs_domain, P, C) | (~ic(C)) | (~ip(P)) | (~((~iext(P, tptp_fun_X_58(C, P), tptp_fun_Y_57(C, P))) | icext(C, tptp_fun_X_58(C, P)))))) | (~((~iext(uri_rdfs_domain, P, C)) | (~((~ic(C)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | icext(C, X)))))))))) | (~((~(iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource) | (~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~((~iext(uri_rdf_type, tptp_fun_X_58(uri_rdfs_Resource, uri_rdf_type), tptp_fun_Y_57(uri_rdfs_Resource, uri_rdf_type))) | icext(uri_rdfs_Resource, tptp_fun_X_58(uri_rdfs_Resource, uri_rdf_type)))))) | (~((~iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource)) | (~((~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X)))))))))),
% 95.75/61.59 inference(quant_inst,[status(thm)],[])).
% 95.75/61.59 tff(194,plain,
% 95.75/61.59 (~((~(iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource) | (~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~((~iext(uri_rdf_type, tptp_fun_X_58(uri_rdfs_Resource, uri_rdf_type), tptp_fun_Y_57(uri_rdfs_Resource, uri_rdf_type))) | icext(uri_rdfs_Resource, tptp_fun_X_58(uri_rdfs_Resource, uri_rdf_type)))))) | (~((~iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource)) | (~((~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X))))))))),
% 95.75/61.59 inference(unit_resolution,[status(thm)],[193, 192])).
% 95.75/61.59 tff(195,plain,
% 95.75/61.59 (((~(iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource) | (~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~((~iext(uri_rdf_type, tptp_fun_X_58(uri_rdfs_Resource, uri_rdf_type), tptp_fun_Y_57(uri_rdfs_Resource, uri_rdf_type))) | icext(uri_rdfs_Resource, tptp_fun_X_58(uri_rdfs_Resource, uri_rdf_type)))))) | (~((~iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource)) | (~((~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X)))))))) | ((~iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource)) | (~((~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X))))))),
% 95.75/61.60 inference(tautology,[status(thm)],[])).
% 95.75/61.60 tff(196,plain,
% 95.75/61.60 ((~iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource)) | (~((~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X)))))),
% 95.75/61.60 inference(unit_resolution,[status(thm)],[195, 194])).
% 95.75/61.60 tff(197,plain,
% 95.75/61.60 (iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource) <=> iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource)),
% 95.75/61.60 inference(rewrite,[status(thm)],[])).
% 95.75/61.60 tff(198,axiom,(iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource)), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','rdfs_type_domain')).
% 95.75/61.60 tff(199,plain,
% 95.75/61.60 (iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource)),
% 95.75/61.60 inference(modus_ponens,[status(thm)],[198, 197])).
% 95.75/61.60 tff(200,plain,
% 95.75/61.60 ((~((~iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource)) | (~((~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X))))))) | (~iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource)) | (~((~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X)))))),
% 95.75/61.60 inference(tautology,[status(thm)],[])).
% 95.75/61.60 tff(201,plain,
% 95.75/61.60 ((~((~iext(uri_rdfs_domain, uri_rdf_type, uri_rdfs_Resource)) | (~((~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X))))))) | (~((~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X)))))),
% 95.75/61.60 inference(unit_resolution,[status(thm)],[200, 199])).
% 95.75/61.60 tff(202,plain,
% 95.75/61.60 (~((~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X))))),
% 95.75/61.60 inference(unit_resolution,[status(thm)],[201, 196])).
% 95.75/61.60 tff(203,plain,
% 95.75/61.60 (((~ic(uri_rdfs_Resource)) | (~ip(uri_rdf_type)) | (~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X)))) | ![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X))),
% 95.75/61.60 inference(tautology,[status(thm)],[])).
% 95.75/61.60 tff(204,plain,
% 95.75/61.60 (![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X))),
% 95.75/61.60 inference(unit_resolution,[status(thm)],[203, 202])).
% 95.75/61.60 tff(205,plain,
% 95.75/61.60 (iext(uri_rdf_type, uri_ex_s, BNODE_x1!143)),
% 95.75/61.60 inference(and_elim,[status(thm)],[7])).
% 95.75/61.60 tff(206,plain,
% 95.75/61.60 (((~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X))) | ((~iext(uri_rdf_type, uri_ex_s, BNODE_x1!143)) | icext(uri_rdfs_Resource, uri_ex_s))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X))) | (~iext(uri_rdf_type, uri_ex_s, BNODE_x1!143)) | icext(uri_rdfs_Resource, uri_ex_s))),
% 95.75/61.60 inference(rewrite,[status(thm)],[])).
% 95.75/61.60 tff(207,plain,
% 95.75/61.60 ((~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X))) | ((~iext(uri_rdf_type, uri_ex_s, BNODE_x1!143)) | icext(uri_rdfs_Resource, uri_ex_s))),
% 95.75/61.60 inference(quant_inst,[status(thm)],[])).
% 95.75/61.60 tff(208,plain,
% 95.75/61.60 ((~![X: $i, Y: $i] : ((~iext(uri_rdf_type, X, Y)) | icext(uri_rdfs_Resource, X))) | (~iext(uri_rdf_type, uri_ex_s, BNODE_x1!143)) | icext(uri_rdfs_Resource, uri_ex_s)),
% 95.75/61.60 inference(modus_ponens,[status(thm)],[207, 206])).
% 95.75/61.60 tff(209,plain,
% 95.75/61.60 (icext(uri_rdfs_Resource, uri_ex_s)),
% 95.75/61.60 inference(unit_resolution,[status(thm)],[208, 205, 204])).
% 95.75/61.60 tff(210,plain,
% 95.75/61.60 (((~![Y: $i] : (ir(Y) | (~icext(uri_rdfs_Resource, Y)))) | (ir(uri_ex_s) | (~icext(uri_rdfs_Resource, uri_ex_s)))) <=> ((~![Y: $i] : (ir(Y) | (~icext(uri_rdfs_Resource, Y)))) | ir(uri_ex_s) | (~icext(uri_rdfs_Resource, uri_ex_s)))),
% 95.75/61.60 inference(rewrite,[status(thm)],[])).
% 95.75/61.60 tff(211,plain,
% 95.75/61.60 ((~![Y: $i] : (ir(Y) | (~icext(uri_rdfs_Resource, Y)))) | (ir(uri_ex_s) | (~icext(uri_rdfs_Resource, uri_ex_s)))),
% 95.75/61.60 inference(quant_inst,[status(thm)],[])).
% 95.75/61.60 tff(212,plain,
% 95.75/61.60 ((~![Y: $i] : (ir(Y) | (~icext(uri_rdfs_Resource, Y)))) | ir(uri_ex_s) | (~icext(uri_rdfs_Resource, uri_ex_s))),
% 95.75/61.60 inference(modus_ponens,[status(thm)],[211, 210])).
% 95.75/61.60 tff(213,plain,
% 95.75/61.60 (ir(uri_ex_s)),
% 95.75/61.60 inference(unit_resolution,[status(thm)],[212, 166, 209])).
% 95.75/61.60 tff(214,plain,
% 95.75/61.60 (iext(uri_owl_onProperty, BNODE_x1!143, uri_ex_p)),
% 95.75/61.60 inference(and_elim,[status(thm)],[7])).
% 95.75/61.60 tff(215,plain,
% 95.75/61.60 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_onProperty, X, Y)) | (~((~ip(Y)) | (~icext(uri_owl_Restriction, X))))) <=> ((~iext(uri_owl_onProperty, X, Y)) | (~((~ip(Y)) | (~icext(uri_owl_Restriction, X))))))),
% 95.75/61.60 inference(bind,[status(th)],[])).
% 95.75/61.60 tff(216,plain,
% 95.75/61.60 (![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~ip(Y)) | (~icext(uri_owl_Restriction, X))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~ip(Y)) | (~icext(uri_owl_Restriction, X)))))),
% 95.75/61.60 inference(quant_intro,[status(thm)],[215])).
% 95.75/61.60 tff(217,plain,
% 95.75/61.60 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_onProperty, X, Y)) | (icext(uri_owl_Restriction, X) & ip(Y))) <=> ((~iext(uri_owl_onProperty, X, Y)) | (~((~ip(Y)) | (~icext(uri_owl_Restriction, X))))))),
% 95.75/61.60 inference(bind,[status(th)],[])).
% 95.75/61.60 tff(218,plain,
% 95.75/61.60 (![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)) | (~((~ip(Y)) | (~icext(uri_owl_Restriction, X)))))),
% 95.75/61.60 inference(quant_intro,[status(thm)],[217])).
% 95.75/61.60 tff(219,plain,
% 95.75/61.60 (![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)))),
% 95.75/61.60 inference(rewrite,[status(thm)],[])).
% 95.75/61.60 tff(220,plain,
% 95.75/61.60 (^[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))))),
% 95.75/61.60 inference(bind,[status(th)],[])).
% 95.75/61.60 tff(221,plain,
% 95.75/61.60 (![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)))),
% 95.75/61.60 inference(quant_intro,[status(thm)],[220])).
% 95.75/61.60 tff(222,axiom,(![X: $i, Y: $i] : (iext(uri_owl_onProperty, X, Y) => (icext(uri_owl_Restriction, X) & ip(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_prop_onproperty_ext')).
% 95.75/61.60 tff(223,plain,
% 95.75/61.60 (![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (icext(uri_owl_Restriction, X) & ip(Y)))),
% 95.75/61.60 inference(modus_ponens,[status(thm)],[222, 221])).
% 95.75/61.60 tff(224,plain,
% 95.75/61.60 (![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (icext(uri_owl_Restriction, X) & ip(Y)))),
% 95.75/61.60 inference(modus_ponens,[status(thm)],[223, 219])).
% 95.75/61.60 tff(225,plain,(
% 95.75/61.60 ![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (icext(uri_owl_Restriction, X) & ip(Y)))),
% 95.75/61.60 inference(skolemize,[status(sab)],[224])).
% 95.75/61.60 tff(226,plain,
% 95.75/61.60 (![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~ip(Y)) | (~icext(uri_owl_Restriction, X)))))),
% 95.75/61.60 inference(modus_ponens,[status(thm)],[225, 218])).
% 95.75/61.60 tff(227,plain,
% 95.75/61.60 (![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~ip(Y)) | (~icext(uri_owl_Restriction, X)))))),
% 95.75/61.60 inference(modus_ponens,[status(thm)],[226, 216])).
% 95.75/61.60 tff(228,plain,
% 95.75/61.60 (((~![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~ip(Y)) | (~icext(uri_owl_Restriction, X)))))) | ((~iext(uri_owl_onProperty, BNODE_x1!143, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~icext(uri_owl_Restriction, BNODE_x1!143)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~ip(Y)) | (~icext(uri_owl_Restriction, X)))))) | (~iext(uri_owl_onProperty, BNODE_x1!143, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~icext(uri_owl_Restriction, BNODE_x1!143)))))),
% 95.75/61.60 inference(rewrite,[status(thm)],[])).
% 95.75/61.60 tff(229,plain,
% 95.75/61.60 ((~![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~ip(Y)) | (~icext(uri_owl_Restriction, X)))))) | ((~iext(uri_owl_onProperty, BNODE_x1!143, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~icext(uri_owl_Restriction, BNODE_x1!143)))))),
% 95.75/61.60 inference(quant_inst,[status(thm)],[])).
% 95.75/61.60 tff(230,plain,
% 95.75/61.60 ((~![X: $i, Y: $i] : ((~iext(uri_owl_onProperty, X, Y)) | (~((~ip(Y)) | (~icext(uri_owl_Restriction, X)))))) | (~iext(uri_owl_onProperty, BNODE_x1!143, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~icext(uri_owl_Restriction, BNODE_x1!143))))),
% 95.75/61.60 inference(modus_ponens,[status(thm)],[229, 228])).
% 95.75/61.60 tff(231,plain,
% 95.75/61.60 (~((~ip(uri_ex_p)) | (~icext(uri_owl_Restriction, BNODE_x1!143)))),
% 95.75/61.60 inference(unit_resolution,[status(thm)],[230, 227, 214])).
% 95.75/61.60 tff(232,plain,
% 95.75/61.60 (((~ip(uri_ex_p)) | (~icext(uri_owl_Restriction, BNODE_x1!143))) | ip(uri_ex_p)),
% 95.75/61.60 inference(tautology,[status(thm)],[])).
% 95.75/61.60 tff(233,plain,
% 95.75/61.60 (ip(uri_ex_p)),
% 95.75/61.60 inference(unit_resolution,[status(thm)],[232, 231])).
% 95.75/61.60 tff(234,plain,
% 95.75/61.60 (^[P: $i, A1: $i, A2: $i] : refl((iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2))))) <=> (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2))))))),
% 95.75/61.60 inference(bind,[status(th)],[])).
% 95.75/61.60 tff(235,plain,
% 95.75/61.60 (![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2))))) <=> ![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))),
% 95.75/61.60 inference(quant_intro,[status(thm)],[234])).
% 95.75/61.60 tff(236,plain,
% 95.75/61.60 (^[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) | (~ip(P)) | (~ir(A1)) | (~ir(A2))))), ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) <=> (~(~(iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2))))))), rewrite((~(~(iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2))))) <=> (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)))), ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) <=> (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2))))), rewrite((iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1) & iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P) & iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)) <=> (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2))))), (((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | (iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1) & iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P) & iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2))) <=> ((iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2))) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2))))))), rewrite(((iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2))) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2))))) <=> (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))), (((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | (iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1) & iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P) & iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2))) <=> (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))))),
% 95.75/61.60 inference(bind,[status(th)],[])).
% 95.75/61.60 tff(237,plain,
% 95.75/61.60 (![P: $i, A1: $i, A2: $i] : ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | (iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1) & iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P) & iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2))) <=> ![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))),
% 95.75/61.60 inference(quant_intro,[status(thm)],[236])).
% 95.75/61.60 tff(238,plain,
% 95.75/61.60 (![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)))),
% 95.75/61.60 inference(rewrite,[status(thm)],[])).
% 95.75/61.60 tff(239,plain,
% 95.75/61.60 (^[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)))))),
% 95.75/61.60 inference(bind,[status(th)],[])).
% 95.75/61.60 tff(240,plain,
% 95.75/61.60 (![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)))),
% 95.75/61.60 inference(quant_intro,[status(thm)],[239])).
% 95.75/61.60 tff(241,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/Axioms/SWB001+0.ax','owl_npa_object_fi')).
% 95.75/61.60 tff(242,plain,
% 95.75/61.60 (![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)))),
% 95.75/61.60 inference(modus_ponens,[status(thm)],[241, 240])).
% 95.75/61.60 tff(243,plain,
% 95.75/61.60 (![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)))),
% 95.75/61.60 inference(modus_ponens,[status(thm)],[242, 238])).
% 95.75/61.60 tff(244,plain,(
% 95.75/61.60 ![P: $i, A1: $i, A2: $i] : ((~(ir(A1) & ip(P) & ir(A2) & (~iext(P, A1, A2)))) | (iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1) & iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P) & iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))),
% 95.75/61.60 inference(skolemize,[status(sab)],[243])).
% 95.75/61.60 tff(245,plain,
% 95.75/61.60 (![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))),
% 95.75/61.60 inference(modus_ponens,[status(thm)],[244, 237])).
% 95.75/61.60 tff(246,plain,
% 95.75/61.60 (![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))),
% 95.75/61.60 inference(modus_ponens,[status(thm)],[245, 235])).
% 95.75/61.60 tff(247,plain,
% 95.75/61.60 (((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))) | ((~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)))))) <=> ((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))) | (~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)))))),
% 95.75/61.60 inference(rewrite,[status(thm)],[])).
% 95.75/61.60 tff(248,plain,
% 95.75/61.60 ((iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | (~((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s))))) <=> ((~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)))))),
% 95.75/61.60 inference(rewrite,[status(thm)],[])).
% 95.75/61.60 tff(249,plain,
% 95.75/61.60 ((~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)))) <=> (~((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s))))),
% 95.75/61.60 inference(rewrite,[status(thm)],[])).
% 95.75/61.60 tff(250,plain,
% 95.75/61.60 ((iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o))))) <=> (iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | (~((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)))))),
% 95.75/61.60 inference(monotonicity,[status(thm)],[249])).
% 95.75/61.60 tff(251,plain,
% 95.75/61.60 ((iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o))))) <=> ((~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)))))),
% 95.75/61.60 inference(transitivity,[status(thm)],[250, 248])).
% 95.75/61.60 tff(252,plain,
% 95.75/61.60 (((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))) | (iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)))))) <=> ((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))) | ((~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s))))))),
% 95.75/61.60 inference(monotonicity,[status(thm)],[251])).
% 95.75/61.60 tff(253,plain,
% 95.75/61.60 (((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))) | (iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)))))) <=> ((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))) | (~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)))))),
% 95.75/61.60 inference(transitivity,[status(thm)],[252, 247])).
% 95.75/61.60 tff(254,plain,
% 95.75/61.60 ((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))) | (iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)))))),
% 95.75/61.60 inference(quant_inst,[status(thm)],[])).
% 95.75/61.60 tff(255,plain,
% 95.75/61.60 ((~![P: $i, A1: $i, A2: $i] : (iext(P, A1, A2) | (~ip(P)) | (~ir(A1)) | (~ir(A2)) | (~((~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(A2, A1, P), A1)) | (~iext(uri_owl_assertionProperty, tptp_fun_Z_139(A2, A1, P), P)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(A2, A1, P), A2)))))) | (~ip(uri_ex_p)) | (~ir(uri_ex_s)) | (~ir(uri_ex_o)) | iext(uri_ex_p, uri_ex_s, uri_ex_o) | (~((~iext(uri_owl_assertionProperty, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_p)) | (~iext(uri_owl_targetIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_o)) | (~iext(uri_owl_sourceIndividual, tptp_fun_Z_139(uri_ex_o, uri_ex_s, uri_ex_p), uri_ex_s))))),
% 95.75/61.60 inference(modus_ponens,[status(thm)],[254, 253])).
% 95.75/61.60 tff(256,plain,
% 95.75/61.60 ($false),
% 95.75/61.60 inference(unit_resolution,[status(thm)],[255, 246, 233, 213, 170, 102, 36])).
% 95.75/61.60 tff(257,plain,(iext(uri_ex_p, uri_ex_s, uri_ex_o)), inference(lemma,lemma(discharge,[]))).
% 95.75/61.60 tff(258,plain,
% 95.75/61.60 (iext(uri_owl_allValuesFrom, BNODE_x1!143, BNODE_x2!142)),
% 95.75/61.60 inference(and_elim,[status(thm)],[7])).
% 95.75/61.60 tff(259,plain,
% 95.75/61.60 (^[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_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))))),
% 95.75/61.60 inference(bind,[status(th)],[])).
% 95.75/61.60 tff(260,plain,
% 95.75/61.60 (![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_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))),
% 95.75/61.60 inference(quant_intro,[status(thm)],[259])).
% 95.75/61.60 tff(261,plain,
% 95.75/61.60 (^[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_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))))),
% 95.75/61.60 inference(bind,[status(th)],[])).
% 95.75/61.60 tff(262,plain,
% 95.75/61.60 (![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_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))),
% 95.75/61.60 inference(quant_intro,[status(thm)],[261])).
% 95.75/61.60 tff(263,plain,
% 95.75/61.60 (![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_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))),
% 95.75/61.60 inference(transitivity,[status(thm)],[262, 260])).
% 95.75/61.60 tff(264,plain,
% 95.75/61.60 (^[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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))) <=> (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))), ((((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))) <=> (((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))) <=> (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P))))))))), ((((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y))) & (icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))) <=> (~((~((~icext(Z, X)) | ![Y: $i] : ((~iext(P, X, Y)) | icext(C, Y)))) | (~(icext(Z, X) | (~((~iext(P, X, tptp_fun_Y_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))))),
% 95.75/61.60 inference(bind,[status(th)],[])).
% 95.75/61.60 tff(265,plain,
% 95.75/61.60 (![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_11(X, C, P))) | icext(C, tptp_fun_Y_11(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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))),
% 95.75/61.60 inference(quant_intro,[status(thm)],[264])).
% 95.75/61.60 tff(266,plain,
% 95.75/61.60 (![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))))),
% 95.75/61.60 inference(rewrite,[status(thm)],[])).
% 95.75/61.60 tff(267,plain,
% 95.75/61.60 (^[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))))))),
% 95.75/61.61 inference(bind,[status(th)],[])).
% 95.75/61.61 tff(268,plain,
% 95.75/61.61 (![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))))),
% 95.75/61.61 inference(quant_intro,[status(thm)],[267])).
% 95.75/61.61 tff(269,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/Axioms/SWB001+0.ax','owl_restrict_allvaluesfrom')).
% 95.75/61.61 tff(270,plain,
% 95.75/61.61 (![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))))),
% 95.75/61.61 inference(modus_ponens,[status(thm)],[269, 268])).
% 95.75/61.61 tff(271,plain,
% 95.75/61.61 (![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))))),
% 95.75/61.61 inference(modus_ponens,[status(thm)],[270, 266])).
% 95.75/61.61 tff(272,plain,(
% 95.75/61.61 ![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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))),
% 95.75/61.61 inference(skolemize,[status(sab)],[271])).
% 95.75/61.61 tff(273,plain,
% 95.75/61.61 (![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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))),
% 95.75/61.61 inference(modus_ponens,[status(thm)],[272, 265])).
% 95.75/61.61 tff(274,plain,
% 95.75/61.61 (![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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))),
% 95.75/61.61 inference(modus_ponens,[status(thm)],[273, 263])).
% 95.75/61.61 tff(275,plain,
% 95.75/61.61 (((~![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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))) | ((~iext(uri_owl_allValuesFrom, BNODE_x1!143, BNODE_x2!142)) | (~iext(uri_owl_onProperty, BNODE_x1!143, uri_ex_p)) | ![X: $i] : (~((~((~icext(BNODE_x1!143, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x2!142, Y)))) | (~(icext(BNODE_x1!143, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_11(X, BNODE_x2!142, uri_ex_p))) | icext(BNODE_x2!142, tptp_fun_Y_11(X, BNODE_x2!142, 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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))) | (~iext(uri_owl_allValuesFrom, BNODE_x1!143, BNODE_x2!142)) | (~iext(uri_owl_onProperty, BNODE_x1!143, uri_ex_p)) | ![X: $i] : (~((~((~icext(BNODE_x1!143, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x2!142, Y)))) | (~(icext(BNODE_x1!143, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_11(X, BNODE_x2!142, uri_ex_p))) | icext(BNODE_x2!142, tptp_fun_Y_11(X, BNODE_x2!142, uri_ex_p)))))))))),
% 95.75/61.61 inference(rewrite,[status(thm)],[])).
% 95.75/61.61 tff(276,plain,
% 95.75/61.61 ((~![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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))) | ((~iext(uri_owl_allValuesFrom, BNODE_x1!143, BNODE_x2!142)) | (~iext(uri_owl_onProperty, BNODE_x1!143, uri_ex_p)) | ![X: $i] : (~((~((~icext(BNODE_x1!143, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x2!142, Y)))) | (~(icext(BNODE_x1!143, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_11(X, BNODE_x2!142, uri_ex_p))) | icext(BNODE_x2!142, tptp_fun_Y_11(X, BNODE_x2!142, uri_ex_p)))))))))),
% 95.75/61.61 inference(quant_inst,[status(thm)],[])).
% 95.75/61.61 tff(277,plain,
% 95.75/61.61 ((~![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_11(X, C, P))) | icext(C, tptp_fun_Y_11(X, C, P)))))))))) | (~iext(uri_owl_allValuesFrom, BNODE_x1!143, BNODE_x2!142)) | (~iext(uri_owl_onProperty, BNODE_x1!143, uri_ex_p)) | ![X: $i] : (~((~((~icext(BNODE_x1!143, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x2!142, Y)))) | (~(icext(BNODE_x1!143, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_11(X, BNODE_x2!142, uri_ex_p))) | icext(BNODE_x2!142, tptp_fun_Y_11(X, BNODE_x2!142, uri_ex_p))))))))),
% 95.75/61.61 inference(modus_ponens,[status(thm)],[276, 275])).
% 95.75/61.61 tff(278,plain,
% 95.75/61.61 (![X: $i] : (~((~((~icext(BNODE_x1!143, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x2!142, Y)))) | (~(icext(BNODE_x1!143, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_11(X, BNODE_x2!142, uri_ex_p))) | icext(BNODE_x2!142, tptp_fun_Y_11(X, BNODE_x2!142, uri_ex_p))))))))),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[277, 274, 214, 258])).
% 95.75/61.61 tff(279,plain,
% 95.75/61.61 ((~![X: $i] : (~((~((~icext(BNODE_x1!143, X)) | ![Y: $i] : ((~iext(uri_ex_p, X, Y)) | icext(BNODE_x2!142, Y)))) | (~(icext(BNODE_x1!143, X) | (~((~iext(uri_ex_p, X, tptp_fun_Y_11(X, BNODE_x2!142, uri_ex_p))) | icext(BNODE_x2!142, tptp_fun_Y_11(X, BNODE_x2!142, uri_ex_p))))))))) | (~((~((~icext(BNODE_x1!143, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y)))) | (~(icext(BNODE_x1!143, uri_ex_s) | (~((~iext(uri_ex_p, uri_ex_s, tptp_fun_Y_11(uri_ex_s, BNODE_x2!142, uri_ex_p))) | icext(BNODE_x2!142, tptp_fun_Y_11(uri_ex_s, BNODE_x2!142, uri_ex_p))))))))),
% 95.75/61.61 inference(quant_inst,[status(thm)],[])).
% 95.75/61.61 tff(280,plain,
% 95.75/61.61 (~((~((~icext(BNODE_x1!143, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y)))) | (~(icext(BNODE_x1!143, uri_ex_s) | (~((~iext(uri_ex_p, uri_ex_s, tptp_fun_Y_11(uri_ex_s, BNODE_x2!142, uri_ex_p))) | icext(BNODE_x2!142, tptp_fun_Y_11(uri_ex_s, BNODE_x2!142, uri_ex_p)))))))),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[279, 278])).
% 95.75/61.61 tff(281,plain,
% 95.75/61.61 (((~((~icext(BNODE_x1!143, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y)))) | (~(icext(BNODE_x1!143, uri_ex_s) | (~((~iext(uri_ex_p, uri_ex_s, tptp_fun_Y_11(uri_ex_s, BNODE_x2!142, uri_ex_p))) | icext(BNODE_x2!142, tptp_fun_Y_11(uri_ex_s, BNODE_x2!142, uri_ex_p))))))) | ((~icext(BNODE_x1!143, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y)))),
% 95.75/61.61 inference(tautology,[status(thm)],[])).
% 95.75/61.61 tff(282,plain,
% 95.75/61.61 ((~icext(BNODE_x1!143, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y))),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[281, 280])).
% 95.75/61.61 tff(283,plain,
% 95.75/61.61 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_s, BNODE_x1!143) <=> icext(BNODE_x1!143, uri_ex_s))),
% 95.75/61.61 inference(quant_inst,[status(thm)],[])).
% 95.75/61.61 tff(284,plain,
% 95.75/61.61 (iext(uri_rdf_type, uri_ex_s, BNODE_x1!143) <=> icext(BNODE_x1!143, uri_ex_s)),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[283, 93])).
% 95.75/61.61 tff(285,plain,
% 95.75/61.61 ((~(iext(uri_rdf_type, uri_ex_s, BNODE_x1!143) <=> icext(BNODE_x1!143, uri_ex_s))) | (~iext(uri_rdf_type, uri_ex_s, BNODE_x1!143)) | icext(BNODE_x1!143, uri_ex_s)),
% 95.75/61.61 inference(tautology,[status(thm)],[])).
% 95.75/61.61 tff(286,plain,
% 95.75/61.61 ((~(iext(uri_rdf_type, uri_ex_s, BNODE_x1!143) <=> icext(BNODE_x1!143, uri_ex_s))) | icext(BNODE_x1!143, uri_ex_s)),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[285, 205])).
% 95.75/61.61 tff(287,plain,
% 95.75/61.61 (icext(BNODE_x1!143, uri_ex_s)),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[286, 284])).
% 95.75/61.61 tff(288,plain,
% 95.75/61.61 ((~((~icext(BNODE_x1!143, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y)))) | (~icext(BNODE_x1!143, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y))),
% 95.75/61.61 inference(tautology,[status(thm)],[])).
% 95.75/61.61 tff(289,plain,
% 95.75/61.61 ((~((~icext(BNODE_x1!143, uri_ex_s)) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y)))) | ![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y))),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[288, 287])).
% 95.75/61.61 tff(290,plain,
% 95.75/61.61 (![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y))),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[289, 282])).
% 95.75/61.61 tff(291,plain,
% 95.75/61.61 (((~![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y))) | ((~iext(uri_ex_p, uri_ex_s, uri_ex_o)) | icext(BNODE_x2!142, uri_ex_o))) <=> ((~![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y))) | (~iext(uri_ex_p, uri_ex_s, uri_ex_o)) | icext(BNODE_x2!142, uri_ex_o))),
% 95.75/61.61 inference(rewrite,[status(thm)],[])).
% 95.75/61.61 tff(292,plain,
% 95.75/61.61 ((~![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y))) | ((~iext(uri_ex_p, uri_ex_s, uri_ex_o)) | icext(BNODE_x2!142, uri_ex_o))),
% 95.75/61.61 inference(quant_inst,[status(thm)],[])).
% 95.75/61.61 tff(293,plain,
% 95.75/61.61 ((~![Y: $i] : ((~iext(uri_ex_p, uri_ex_s, Y)) | icext(BNODE_x2!142, Y))) | (~iext(uri_ex_p, uri_ex_s, uri_ex_o)) | icext(BNODE_x2!142, uri_ex_o)),
% 95.75/61.61 inference(modus_ponens,[status(thm)],[292, 291])).
% 95.75/61.61 tff(294,plain,
% 95.75/61.61 (icext(BNODE_x2!142, uri_ex_o)),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[293, 290, 257])).
% 95.75/61.61 tff(295,plain,
% 95.75/61.61 ((~(icext(BNODE_x2!142, uri_ex_o) <=> (~icext(BNODE_x3!141, uri_ex_o)))) | (~icext(BNODE_x2!142, uri_ex_o)) | (~icext(BNODE_x3!141, uri_ex_o))),
% 95.75/61.61 inference(tautology,[status(thm)],[])).
% 95.75/61.61 tff(296,plain,
% 95.75/61.61 ((~(icext(BNODE_x2!142, uri_ex_o) <=> (~icext(BNODE_x3!141, uri_ex_o)))) | (~icext(BNODE_x3!141, uri_ex_o))),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[295, 294])).
% 95.75/61.61 tff(297,plain,
% 95.75/61.61 (~icext(BNODE_x3!141, uri_ex_o)),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[296, 35])).
% 95.75/61.61 tff(298,plain,
% 95.75/61.61 (iext(uri_rdf_rest, BNODE_x4!140, uri_rdf_nil)),
% 95.75/61.61 inference(and_elim,[status(thm)],[7])).
% 95.75/61.61 tff(299,plain,
% 95.75/61.61 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))))))))),
% 95.75/61.61 inference(bind,[status(th)],[])).
% 95.75/61.61 tff(300,plain,
% 95.75/61.61 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 95.75/61.61 inference(quant_intro,[status(thm)],[299])).
% 95.75/61.61 tff(301,plain,
% 95.75/61.61 (^[Z: $i, S1: $i, A1: $i] : refl(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 95.75/61.61 inference(bind,[status(th)],[])).
% 95.75/61.61 tff(302,plain,
% 95.75/61.61 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 95.75/61.61 inference(quant_intro,[status(thm)],[301])).
% 95.75/61.61 tff(303,plain,
% 95.75/61.61 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 95.75/61.61 inference(bind,[status(th)],[])).
% 95.75/61.61 tff(304,plain,
% 95.75/61.61 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 95.75/61.61 inference(quant_intro,[status(thm)],[303])).
% 95.75/61.61 tff(305,plain,
% 95.75/61.61 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 95.75/61.61 inference(transitivity,[status(thm)],[304, 302])).
% 95.75/61.61 tff(306,plain,
% 95.75/61.61 (^[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))))))), rewrite((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))), rewrite((((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> (((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))))), rewrite((((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))))),
% 95.75/61.61 inference(bind,[status(th)],[])).
% 95.75/61.61 tff(307,plain,
% 95.75/61.61 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 95.75/61.61 inference(quant_intro,[status(thm)],[306])).
% 95.75/61.61 tff(308,plain,
% 95.75/61.61 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1))))))),
% 95.75/61.61 inference(bind,[status(th)],[])).
% 95.75/61.61 tff(309,plain,
% 95.75/61.61 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))),
% 95.75/61.61 inference(quant_intro,[status(thm)],[308])).
% 95.75/61.61 tff(310,plain,
% 95.75/61.61 (![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)))))),
% 95.75/61.61 inference(rewrite,[status(thm)],[])).
% 95.75/61.61 tff(311,plain,
% 95.75/61.61 (^[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)))))))),
% 95.75/61.61 inference(bind,[status(th)],[])).
% 95.75/61.61 tff(312,plain,
% 95.75/61.61 (![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)))))),
% 95.75/61.61 inference(quant_intro,[status(thm)],[311])).
% 95.75/61.61 tff(313,axiom,(![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_enum_class_001')).
% 95.75/61.61 tff(314,plain,
% 95.75/61.61 (![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)))))),
% 95.75/61.61 inference(modus_ponens,[status(thm)],[313, 312])).
% 95.75/61.61 tff(315,plain,
% 95.75/61.61 (![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)))))),
% 95.75/61.61 inference(modus_ponens,[status(thm)],[314, 310])).
% 95.75/61.61 tff(316,plain,(
% 95.75/61.61 ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 95.75/61.61 inference(skolemize,[status(sab)],[315])).
% 95.75/61.61 tff(317,plain,
% 95.75/61.61 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))),
% 95.75/61.61 inference(modus_ponens,[status(thm)],[316, 309])).
% 95.75/61.61 tff(318,plain,
% 95.75/61.61 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 95.75/61.61 inference(modus_ponens,[status(thm)],[317, 307])).
% 95.75/61.61 tff(319,plain,
% 95.75/61.61 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 95.75/61.61 inference(modus_ponens,[status(thm)],[318, 305])).
% 95.75/61.61 tff(320,plain,
% 95.75/61.61 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 95.75/61.61 inference(modus_ponens,[status(thm)],[319, 300])).
% 95.75/61.61 tff(321,plain,
% 95.75/61.61 (((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, BNODE_x4!140, uri_ex_o)) | (~iext(uri_rdf_rest, BNODE_x4!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140) | (~ic(BNODE_x3!141)) | ((~icext(BNODE_x3!141, tptp_fun_X_8(uri_ex_o, BNODE_x3!141))) <=> (tptp_fun_X_8(uri_ex_o, BNODE_x3!141) = uri_ex_o)))) | (~((~iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140)) | (~((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, 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_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, BNODE_x4!140, uri_ex_o)) | (~iext(uri_rdf_rest, BNODE_x4!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140) | (~ic(BNODE_x3!141)) | ((~icext(BNODE_x3!141, tptp_fun_X_8(uri_ex_o, BNODE_x3!141))) <=> (tptp_fun_X_8(uri_ex_o, BNODE_x3!141) = uri_ex_o)))) | (~((~iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140)) | (~((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))))))))))),
% 95.75/61.61 inference(rewrite,[status(thm)],[])).
% 95.75/61.61 tff(322,plain,
% 95.75/61.61 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, BNODE_x4!140, uri_ex_o)) | (~iext(uri_rdf_rest, BNODE_x4!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140) | (~ic(BNODE_x3!141)) | ((~icext(BNODE_x3!141, tptp_fun_X_8(uri_ex_o, BNODE_x3!141))) <=> (tptp_fun_X_8(uri_ex_o, BNODE_x3!141) = uri_ex_o)))) | (~((~iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140)) | (~((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))))))))))),
% 95.75/61.61 inference(quant_inst,[status(thm)],[])).
% 95.75/61.61 tff(323,plain,
% 95.75/61.61 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_8(A1, Z))) <=> (tptp_fun_X_8(A1, Z) = A1)))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, BNODE_x4!140, uri_ex_o)) | (~iext(uri_rdf_rest, BNODE_x4!140, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140) | (~ic(BNODE_x3!141)) | ((~icext(BNODE_x3!141, tptp_fun_X_8(uri_ex_o, BNODE_x3!141))) <=> (tptp_fun_X_8(uri_ex_o, BNODE_x3!141) = uri_ex_o)))) | (~((~iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140)) | (~((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o)))))))))),
% 95.75/61.61 inference(modus_ponens,[status(thm)],[322, 321])).
% 95.75/61.61 tff(324,plain,
% 95.75/61.61 (~((~(iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140) | (~ic(BNODE_x3!141)) | ((~icext(BNODE_x3!141, tptp_fun_X_8(uri_ex_o, BNODE_x3!141))) <=> (tptp_fun_X_8(uri_ex_o, BNODE_x3!141) = uri_ex_o)))) | (~((~iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140)) | (~((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))))))))),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[323, 320, 142, 298])).
% 95.75/61.61 tff(325,plain,
% 95.75/61.61 (((~(iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140) | (~ic(BNODE_x3!141)) | ((~icext(BNODE_x3!141, tptp_fun_X_8(uri_ex_o, BNODE_x3!141))) <=> (tptp_fun_X_8(uri_ex_o, BNODE_x3!141) = uri_ex_o)))) | (~((~iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140)) | (~((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o)))))))) | ((~iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140)) | (~((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))))))),
% 95.75/61.61 inference(tautology,[status(thm)],[])).
% 95.75/61.61 tff(326,plain,
% 95.75/61.61 ((~iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140)) | (~((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o)))))),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[325, 324])).
% 95.75/61.61 tff(327,plain,
% 95.75/61.61 (iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140)),
% 95.75/61.61 inference(and_elim,[status(thm)],[7])).
% 95.75/61.61 tff(328,plain,
% 95.75/61.61 ((~((~iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140)) | (~((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))))))) | (~iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140)) | (~((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o)))))),
% 95.75/61.61 inference(tautology,[status(thm)],[])).
% 95.75/61.61 tff(329,plain,
% 95.75/61.61 ((~((~iext(uri_owl_oneOf, BNODE_x3!141, BNODE_x4!140)) | (~((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))))))) | (~((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o)))))),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[328, 327])).
% 95.75/61.61 tff(330,plain,
% 95.75/61.61 (~((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))))),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[329, 326])).
% 95.75/61.61 tff(331,plain,
% 95.75/61.61 (((~ic(BNODE_x3!141)) | (~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o)))) | ![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))),
% 95.75/61.61 inference(tautology,[status(thm)],[])).
% 95.75/61.61 tff(332,plain,
% 95.75/61.61 (![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))),
% 95.75/61.61 inference(unit_resolution,[status(thm)],[331, 330])).
% 95.91/61.79 tff(333,plain,
% 95.91/61.79 (((~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))) | icext(BNODE_x3!141, uri_ex_o)) <=> ((~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))) | icext(BNODE_x3!141, uri_ex_o))),
% 95.91/61.79 inference(rewrite,[status(thm)],[])).
% 95.91/61.79 tff(334,plain,
% 95.91/61.79 ((icext(BNODE_x3!141, uri_ex_o) <=> $true) <=> icext(BNODE_x3!141, uri_ex_o)),
% 95.91/61.79 inference(rewrite,[status(thm)],[])).
% 95.91/61.79 tff(335,plain,
% 95.91/61.79 ((uri_ex_o = uri_ex_o) <=> $true),
% 95.91/61.79 inference(rewrite,[status(thm)],[])).
% 95.91/61.79 tff(336,plain,
% 95.91/61.79 ((icext(BNODE_x3!141, uri_ex_o) <=> (uri_ex_o = uri_ex_o)) <=> (icext(BNODE_x3!141, uri_ex_o) <=> $true)),
% 95.91/61.79 inference(monotonicity,[status(thm)],[335])).
% 95.91/61.79 tff(337,plain,
% 95.91/61.79 ((icext(BNODE_x3!141, uri_ex_o) <=> (uri_ex_o = uri_ex_o)) <=> icext(BNODE_x3!141, uri_ex_o)),
% 95.91/61.79 inference(transitivity,[status(thm)],[336, 334])).
% 95.91/61.79 tff(338,plain,
% 95.91/61.79 (((~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))) | (icext(BNODE_x3!141, uri_ex_o) <=> (uri_ex_o = uri_ex_o))) <=> ((~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))) | icext(BNODE_x3!141, uri_ex_o))),
% 95.91/61.79 inference(monotonicity,[status(thm)],[337])).
% 95.91/61.79 tff(339,plain,
% 95.91/61.79 (((~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))) | (icext(BNODE_x3!141, uri_ex_o) <=> (uri_ex_o = uri_ex_o))) <=> ((~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))) | icext(BNODE_x3!141, uri_ex_o))),
% 95.91/61.79 inference(transitivity,[status(thm)],[338, 333])).
% 95.91/61.79 tff(340,plain,
% 95.91/61.79 ((~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))) | (icext(BNODE_x3!141, uri_ex_o) <=> (uri_ex_o = uri_ex_o))),
% 95.91/61.79 inference(quant_inst,[status(thm)],[])).
% 95.91/61.79 tff(341,plain,
% 95.91/61.79 ((~![X: $i] : (icext(BNODE_x3!141, X) <=> (X = uri_ex_o))) | icext(BNODE_x3!141, uri_ex_o)),
% 95.91/61.79 inference(modus_ponens,[status(thm)],[340, 339])).
% 95.91/61.79 tff(342,plain,
% 95.91/61.79 ($false),
% 95.91/61.79 inference(unit_resolution,[status(thm)],[341, 332, 297])).
% 95.91/61.79 % SZS output end Proof
%------------------------------------------------------------------------------