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Z3---4.15.1.THM-Prf.s

View TPTP
Problem Process solution in
SystemOnTSTP Download .tgz 
%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : SWB025+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 05:29:39 AM UTC 2025

% Result   : Theorem 0.67s 0.86s
% Output   : Proof 0.67s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SWB025+1 : TPTP v9.0.0. Released v5.2.0.
% 0.04/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n004.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   : Fri Jun 20 07:51:38 EDT 2025
% 0.12/0.33  % CPUTime    : 
% 0.67/0.86  % SZS status Theorem
% 0.67/0.86  % SZS output start Proof
% 0.67/0.86  tff(iext_type, type, (
% 0.67/0.86     iext: ( $i * $i * $i ) > $o)).
% 0.67/0.86  tff(uri_ex_hasUncle_type, type, (
% 0.67/0.86     uri_ex_hasUncle: $i)).
% 0.67/0.86  tff(uri_ex_hasCousin_type, type, (
% 0.67/0.86     uri_ex_hasCousin: $i)).
% 0.67/0.86  tff(uri_ex_hasFather_type, type, (
% 0.67/0.86     uri_ex_hasFather: $i)).
% 0.67/0.86  tff(ip_type, type, (
% 0.67/0.86     ip: $i > $o)).
% 0.67/0.86  tff(tptp_fun_BNODE_l11_144_type, type, (
% 0.67/0.86     tptp_fun_BNODE_l11_144: $i)).
% 0.67/0.86  tff(uri_owl_propertyChainAxiom_type, type, (
% 0.67/0.86     uri_owl_propertyChainAxiom: $i)).
% 0.67/0.86  tff(tptp_fun_Y2_100_type, type, (
% 0.67/0.86     tptp_fun_Y2_100: ( $i * $i * $i ) > $i)).
% 0.67/0.86  tff(tptp_fun_Y0_102_type, type, (
% 0.67/0.86     tptp_fun_Y0_102: ( $i * $i * $i ) > $i)).
% 0.67/0.86  tff(tptp_fun_Y1_101_type, type, (
% 0.67/0.86     tptp_fun_Y1_101: ( $i * $i * $i ) > $i)).
% 0.67/0.86  tff(uri_rdf_nil_type, type, (
% 0.67/0.86     uri_rdf_nil: $i)).
% 0.67/0.86  tff(tptp_fun_BNODE_l12_143_type, type, (
% 0.67/0.86     tptp_fun_BNODE_l12_143: $i)).
% 0.67/0.86  tff(uri_rdf_rest_type, type, (
% 0.67/0.86     uri_rdf_rest: $i)).
% 0.67/0.86  tff(uri_ex_dave_type, type, (
% 0.67/0.86     uri_ex_dave: $i)).
% 0.67/0.86  tff(uri_ex_bob_type, type, (
% 0.67/0.86     uri_ex_bob: $i)).
% 0.67/0.86  tff(uri_ex_charly_type, type, (
% 0.67/0.86     uri_ex_charly: $i)).
% 0.67/0.86  tff(uri_ex_alice_type, type, (
% 0.67/0.86     uri_ex_alice: $i)).
% 0.67/0.86  tff(tptp_fun_BNODE_l3_140_type, type, (
% 0.67/0.86     tptp_fun_BNODE_l3_140: $i)).
% 0.67/0.86  tff(uri_owl_inverseOf_type, type, (
% 0.67/0.86     uri_owl_inverseOf: $i)).
% 0.67/0.86  tff(tptp_fun_BNODE_l22_141_type, type, (
% 0.67/0.86     tptp_fun_BNODE_l22_141: $i)).
% 0.67/0.86  tff(uri_rdf_first_type, type, (
% 0.67/0.86     uri_rdf_first: $i)).
% 0.67/0.86  tff(tptp_fun_BNODE_l21_142_type, type, (
% 0.67/0.86     tptp_fun_BNODE_l21_142: $i)).
% 0.67/0.86  tff(tptp_fun_X_108_type, type, (
% 0.67/0.86     tptp_fun_X_108: ( $i * $i ) > $i)).
% 0.67/0.86  tff(tptp_fun_Y_107_type, type, (
% 0.67/0.86     tptp_fun_Y_107: ( $i * $i ) > $i)).
% 0.67/0.86  tff(1,plain,
% 0.67/0.86      (?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l3: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) <=> ?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l3: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave))),
% 0.67/0.86      inference(rewrite,[status(thm)],[])).
% 0.67/0.86  tff(2,plain,
% 0.67/0.86      (^[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12))), ((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) <=> ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather))), ((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)))), (((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) <=> ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil))), (((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)))), ((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) <=> ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21))), ((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)))), (((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) <=> ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle))), (((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)))), ((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) <=> ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22))), ((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)))), (((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) <=> ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3))), (((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)))), ((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) <=> ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil))), ((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)))), (((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) <=> ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather))), (((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)))), ((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) <=> ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))), ((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)))), (((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) <=> ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob))), (((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)))), ((((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) <=> ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly))), ((((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)))), (((((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) <=> ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)))), rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave))), (((((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(3,plain,
% 0.67/0.87      (?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l3: $i] : ((((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) <=> ?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l3: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[2])).
% 0.67/0.87  tff(4,axiom,(?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l3: $i] : ((((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_premise_fullish_025_Cyclic_Dependencies_between_Complex_Properties')).
% 0.67/0.87  tff(5,plain,
% 0.67/0.87      (?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l3: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[4, 3])).
% 0.67/0.87  tff(6,plain,
% 0.67/0.87      (?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l3: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, BNODE_l3) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave))),
% 0.67/0.87      inference(modus_ponens,[status(thm)],[5, 1])).
% 0.67/0.87  tff(7,plain,(
% 0.67/0.87      iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) & iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143) & iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) & iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141) & iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140) & iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)),
% 0.67/0.87      inference(skolemize,[status(sab)],[6])).
% 0.67/0.87  tff(8,plain,
% 0.67/0.87      (iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)),
% 0.67/0.87      inference(and_elim,[status(thm)],[7])).
% 0.67/0.87  tff(9,plain,
% 0.67/0.87      (iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)),
% 0.67/0.87      inference(and_elim,[status(thm)],[7])).
% 0.67/0.87  tff(10,plain,
% 0.67/0.87      (iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)),
% 0.67/0.87      inference(and_elim,[status(thm)],[7])).
% 0.67/0.87  tff(11,plain,
% 0.67/0.87      (iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)),
% 0.67/0.87      inference(and_elim,[status(thm)],[7])).
% 0.67/0.87  tff(12,plain,
% 0.67/0.87      (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))))))), (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))))))))), rewrite(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))), (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(13,plain,
% 0.67/0.87      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[12])).
% 0.67/0.87  tff(14,plain,
% 0.67/0.87      (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : refl(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(15,plain,
% 0.67/0.87      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[14])).
% 0.67/0.87  tff(16,plain,
% 0.67/0.87      (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : rewrite(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))))),
% 0.67/0.87      inference(bind,[status(th)],[])).
% 0.67/0.87  tff(17,plain,
% 0.67/0.87      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.67/0.87      inference(quant_intro,[status(thm)],[16])).
% 0.67/0.87  tff(18,plain,
% 0.67/0.87      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.67/0.88      inference(transitivity,[status(thm)],[17, 15])).
% 0.67/0.88  tff(19,plain,
% 0.67/0.88      (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) <=> ((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))), trans(monotonicity(rewrite((~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) <=> (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))) <=> (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))), rewrite((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) <=> (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))))), rewrite((((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))))),
% 0.67/0.88      inference(bind,[status(th)],[])).
% 0.67/0.88  tff(20,plain,
% 0.67/0.88      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.67/0.88      inference(quant_intro,[status(thm)],[19])).
% 0.67/0.88  tff(21,plain,
% 0.67/0.88      (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : rewrite(((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))),
% 0.67/0.88      inference(bind,[status(th)],[])).
% 0.67/0.88  tff(22,plain,
% 0.67/0.88      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))),
% 0.67/0.88      inference(quant_intro,[status(thm)],[21])).
% 0.67/0.88  tff(23,plain,
% 0.67/0.88      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.67/0.88      inference(rewrite,[status(thm)],[])).
% 0.67/0.88  tff(24,plain,
% 0.67/0.88      (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2))), ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))), ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2)))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))), (((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2))))) <=> ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))))), rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))), (((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))))),
% 0.67/0.88      inference(bind,[status(th)],[])).
% 0.67/0.88  tff(25,plain,
% 0.67/0.88      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.67/0.88      inference(quant_intro,[status(thm)],[24])).
% 0.67/0.88  tff(26,axiom,(![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_chain_002')).
% 0.67/0.88  tff(27,plain,
% 0.67/0.88      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[26, 25])).
% 0.67/0.88  tff(28,plain,
% 0.67/0.88      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[27, 23])).
% 0.67/0.88  tff(29,plain,(
% 0.67/0.88      ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))),
% 0.67/0.88      inference(skolemize,[status(sab)],[28])).
% 0.67/0.88  tff(30,plain,
% 0.67/0.88      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[29, 22])).
% 0.67/0.88  tff(31,plain,
% 0.67/0.88      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[30, 20])).
% 0.67/0.88  tff(32,plain,
% 0.67/0.88      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[31, 18])).
% 0.67/0.88  tff(33,plain,
% 0.67/0.88      (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))),
% 0.67/0.88      inference(modus_ponens,[status(thm)],[32, 13])).
% 0.67/0.88  tff(34,plain,
% 0.67/0.88      (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))))),
% 0.67/0.88      inference(rewrite,[status(thm)],[])).
% 0.67/0.88  tff(35,plain,
% 0.67/0.88      (((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))))),
% 0.67/0.88      inference(rewrite,[status(thm)],[])).
% 0.67/0.88  tff(36,plain,
% 0.67/0.88      ((~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))))))),
% 0.67/0.89      inference(rewrite,[status(thm)],[])).
% 0.67/0.89  tff(37,plain,
% 0.67/0.89      (((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))))),
% 0.67/0.89      inference(monotonicity,[status(thm)],[36])).
% 0.67/0.89  tff(38,plain,
% 0.67/0.89      (((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))))),
% 0.67/0.89      inference(transitivity,[status(thm)],[37, 35])).
% 0.67/0.89  tff(39,plain,
% 0.67/0.89      (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))))))))),
% 0.67/0.89      inference(monotonicity,[status(thm)],[38])).
% 0.67/0.89  tff(40,plain,
% 0.67/0.89      (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))))),
% 0.67/0.89      inference(transitivity,[status(thm)],[39, 34])).
% 0.67/0.89  tff(41,plain,
% 0.67/0.89      ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)))))))))))),
% 0.67/0.89      inference(quant_inst,[status(thm)],[])).
% 0.67/0.89  tff(42,plain,
% 0.67/0.89      ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))))))),
% 0.67/0.89      inference(modus_ponens,[status(thm)],[41, 40])).
% 0.67/0.89  tff(43,plain,
% 0.67/0.89      (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))),
% 0.67/0.89      inference(unit_resolution,[status(thm)],[42, 33, 11, 10, 9, 8])).
% 0.67/0.89  tff(44,plain,
% 0.67/0.89      (((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))))) | ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))),
% 0.67/0.89      inference(tautology,[status(thm)],[])).
% 0.67/0.89  tff(45,plain,
% 0.67/0.89      ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))),
% 0.67/0.89      inference(unit_resolution,[status(thm)],[44, 43])).
% 0.67/0.89  tff(46,plain,
% 0.67/0.89      (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)),
% 0.67/0.89      inference(and_elim,[status(thm)],[7])).
% 0.67/0.89  tff(47,plain,
% 0.67/0.89      ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))) | (~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))),
% 0.67/0.89      inference(tautology,[status(thm)],[])).
% 0.67/0.89  tff(48,plain,
% 0.67/0.89      ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))),
% 0.67/0.89      inference(unit_resolution,[status(thm)],[47, 46])).
% 0.67/0.89  tff(49,plain,
% 0.67/0.89      (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))),
% 0.67/0.89      inference(unit_resolution,[status(thm)],[48, 45])).
% 0.67/0.89  tff(50,plain,
% 0.67/0.89      (((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))) | ![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))),
% 0.67/0.89      inference(tautology,[status(thm)],[])).
% 0.67/0.89  tff(51,plain,
% 0.67/0.89      (![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))),
% 0.67/0.89      inference(unit_resolution,[status(thm)],[50, 49])).
% 0.67/0.89  tff(52,plain,
% 0.67/0.89      (iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)),
% 0.67/0.89      inference(and_elim,[status(thm)],[7])).
% 0.67/0.89  tff(53,plain,
% 0.67/0.89      (iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)),
% 0.67/0.89      inference(and_elim,[status(thm)],[7])).
% 0.67/0.89  tff(54,plain,
% 0.67/0.89      (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))))))),
% 0.67/0.89      inference(bind,[status(th)],[])).
% 0.67/0.89  tff(55,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.67/0.89      inference(quant_intro,[status(thm)],[54])).
% 0.67/0.89  tff(56,plain,
% 0.67/0.89      (^[P1: $i, P2: $i] : refl((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))))),
% 0.67/0.89      inference(bind,[status(th)],[])).
% 0.67/0.89  tff(57,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.67/0.89      inference(quant_intro,[status(thm)],[56])).
% 0.67/0.89  tff(58,plain,
% 0.67/0.89      (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))))),
% 0.67/0.89      inference(bind,[status(th)],[])).
% 0.67/0.89  tff(59,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.67/0.89      inference(quant_intro,[status(thm)],[58])).
% 0.67/0.89  tff(60,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.67/0.89      inference(transitivity,[status(thm)],[59, 57])).
% 0.67/0.89  tff(61,plain,
% 0.67/0.89      (^[P1: $i, P2: $i] : trans(monotonicity(rewrite(((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))), trans(monotonicity(rewrite((~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))) <=> (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))), ((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))), rewrite((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))), ((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))), ((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) <=> (((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))), rewrite((((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))), ((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))))),
% 0.67/0.89      inference(bind,[status(th)],[])).
% 0.67/0.89  tff(62,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.67/0.89      inference(quant_intro,[status(thm)],[61])).
% 0.67/0.89  tff(63,plain,
% 0.67/0.89      (^[P1: $i, P2: $i] : rewrite((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))),
% 0.67/0.89      inference(bind,[status(th)],[])).
% 0.67/0.89  tff(64,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> ![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))),
% 0.67/0.89      inference(quant_intro,[status(thm)],[63])).
% 0.67/0.89  tff(65,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.67/0.89      inference(rewrite,[status(thm)],[])).
% 0.67/0.89  tff(66,plain,
% 0.67/0.89      (^[P1: $i, P2: $i] : rewrite((iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))),
% 0.67/0.89      inference(bind,[status(th)],[])).
% 0.67/0.89  tff(67,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) <=> ![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.67/0.89      inference(quant_intro,[status(thm)],[66])).
% 0.67/0.89  tff(68,axiom,(![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_inv')).
% 0.67/0.89  tff(69,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.67/0.89      inference(modus_ponens,[status(thm)],[68, 67])).
% 0.67/0.89  tff(70,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))),
% 0.67/0.89      inference(modus_ponens,[status(thm)],[69, 65])).
% 0.67/0.89  tff(71,plain,(
% 0.67/0.89      ![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))),
% 0.67/0.89      inference(skolemize,[status(sab)],[70])).
% 0.67/0.89  tff(72,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))),
% 0.67/0.89      inference(modus_ponens,[status(thm)],[71, 64])).
% 0.67/0.89  tff(73,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.67/0.89      inference(modus_ponens,[status(thm)],[72, 62])).
% 0.67/0.89  tff(74,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.67/0.89      inference(modus_ponens,[status(thm)],[73, 60])).
% 0.67/0.89  tff(75,plain,
% 0.67/0.89      (![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.67/0.89      inference(modus_ponens,[status(thm)],[74, 55])).
% 0.67/0.89  tff(76,plain,
% 0.67/0.89      ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather) | (~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~(iext(BNODE_l3!140, tptp_fun_X_108(uri_ex_hasFather, BNODE_l3!140), tptp_fun_Y_107(uri_ex_hasFather, BNODE_l3!140)) <=> iext(uri_ex_hasFather, tptp_fun_Y_107(uri_ex_hasFather, BNODE_l3!140), tptp_fun_X_108(uri_ex_hasFather, BNODE_l3!140)))))) | (~((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))))))),
% 0.67/0.89      inference(quant_inst,[status(thm)],[])).
% 0.67/0.89  tff(77,plain,
% 0.67/0.89      (~((~(iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather) | (~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~(iext(BNODE_l3!140, tptp_fun_X_108(uri_ex_hasFather, BNODE_l3!140), tptp_fun_Y_107(uri_ex_hasFather, BNODE_l3!140)) <=> iext(uri_ex_hasFather, tptp_fun_Y_107(uri_ex_hasFather, BNODE_l3!140), tptp_fun_X_108(uri_ex_hasFather, BNODE_l3!140)))))) | (~((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))))))))),
% 0.67/0.89      inference(unit_resolution,[status(thm)],[76, 75])).
% 0.67/0.89  tff(78,plain,
% 0.67/0.89      (((~(iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather) | (~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~(iext(BNODE_l3!140, tptp_fun_X_108(uri_ex_hasFather, BNODE_l3!140), tptp_fun_Y_107(uri_ex_hasFather, BNODE_l3!140)) <=> iext(uri_ex_hasFather, tptp_fun_Y_107(uri_ex_hasFather, BNODE_l3!140), tptp_fun_X_108(uri_ex_hasFather, BNODE_l3!140)))))) | (~((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))))) | ((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))))))),
% 0.67/0.89      inference(tautology,[status(thm)],[])).
% 0.67/0.89  tff(79,plain,
% 0.67/0.89      ((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))),
% 0.67/0.89      inference(unit_resolution,[status(thm)],[78, 77])).
% 0.67/0.89  tff(80,plain,
% 0.67/0.89      (iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)),
% 0.67/0.89      inference(and_elim,[status(thm)],[7])).
% 0.67/0.89  tff(81,plain,
% 0.67/0.89      ((~((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))))))) | (~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))),
% 0.67/0.90      inference(tautology,[status(thm)],[])).
% 0.67/0.90  tff(82,plain,
% 0.67/0.90      ((~((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))))))) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))),
% 0.67/0.90      inference(unit_resolution,[status(thm)],[81, 80])).
% 0.67/0.90  tff(83,plain,
% 0.67/0.90      (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))))),
% 0.67/0.90      inference(unit_resolution,[status(thm)],[82, 79])).
% 0.67/0.90  tff(84,plain,
% 0.67/0.90      (((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X)))) | ![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))),
% 0.67/0.90      inference(tautology,[status(thm)],[])).
% 0.67/0.90  tff(85,plain,
% 0.67/0.90      (![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))),
% 0.67/0.90      inference(unit_resolution,[status(thm)],[84, 83])).
% 0.67/0.90  tff(86,plain,
% 0.67/0.90      ((~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))) | (iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))),
% 0.67/0.90      inference(quant_inst,[status(thm)],[])).
% 0.67/0.90  tff(87,plain,
% 0.67/0.90      (iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)),
% 0.67/0.90      inference(unit_resolution,[status(thm)],[86, 85])).
% 0.67/0.90  tff(88,plain,
% 0.67/0.90      (iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)),
% 0.67/0.90      inference(and_elim,[status(thm)],[7])).
% 0.67/0.90  tff(89,plain,
% 0.67/0.90      ((~(iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))) | iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice) | (~iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))),
% 0.67/0.90      inference(tautology,[status(thm)],[])).
% 0.67/0.90  tff(90,plain,
% 0.67/0.90      ((~(iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))) | iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice)),
% 0.67/0.90      inference(unit_resolution,[status(thm)],[89, 88])).
% 0.67/0.90  tff(91,plain,
% 0.67/0.90      (iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice)),
% 0.67/0.90      inference(unit_resolution,[status(thm)],[90, 87])).
% 0.67/0.90  tff(92,plain,
% 0.67/0.90      (iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)),
% 0.67/0.90      inference(and_elim,[status(thm)],[7])).
% 0.67/0.90  tff(93,plain,
% 0.67/0.90      (iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)),
% 0.67/0.90      inference(and_elim,[status(thm)],[7])).
% 0.67/0.90  tff(94,plain,
% 0.67/0.90      (iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)),
% 0.67/0.90      inference(and_elim,[status(thm)],[7])).
% 0.67/0.90  tff(95,plain,
% 0.67/0.90      (iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)),
% 0.67/0.90      inference(and_elim,[status(thm)],[7])).
% 0.67/0.90  tff(96,plain,
% 0.67/0.90      (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~((~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~((~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))))),
% 0.67/0.90      inference(rewrite,[status(thm)],[])).
% 0.67/0.90  tff(97,plain,
% 0.67/0.90      (((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~((~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~((~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))))),
% 0.67/0.90      inference(rewrite,[status(thm)],[])).
% 0.67/0.90  tff(98,plain,
% 0.67/0.90      ((~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~((~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))))))),
% 0.67/0.90      inference(rewrite,[status(thm)],[])).
% 0.67/0.90  tff(99,plain,
% 0.67/0.90      (((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~((~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))))),
% 0.67/0.90      inference(monotonicity,[status(thm)],[98])).
% 0.67/0.90  tff(100,plain,
% 0.67/0.90      (((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~((~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))))),
% 0.67/0.90      inference(transitivity,[status(thm)],[99, 97])).
% 0.67/0.90  tff(101,plain,
% 0.67/0.90      (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~((~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))))))))),
% 0.67/0.90      inference(monotonicity,[status(thm)],[100])).
% 0.67/0.90  tff(102,plain,
% 0.67/0.90      (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~((~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))))),
% 0.67/0.90      inference(transitivity,[status(thm)],[101, 96])).
% 0.67/0.90  tff(103,plain,
% 0.67/0.90      ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)))))))))))),
% 0.67/0.90      inference(quant_inst,[status(thm)],[])).
% 0.67/0.90  tff(104,plain,
% 0.67/0.90      ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~((~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))))))),
% 0.67/0.90      inference(modus_ponens,[status(thm)],[103, 102])).
% 0.67/0.90  tff(105,plain,
% 0.67/0.90      (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~((~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))),
% 0.67/0.90      inference(unit_resolution,[status(thm)],[104, 33, 95, 94, 93, 92])).
% 0.67/0.90  tff(106,plain,
% 0.67/0.90      (((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~((~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))))) | ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))),
% 0.67/0.90      inference(tautology,[status(thm)],[])).
% 0.67/0.90  tff(107,plain,
% 0.67/0.90      ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))),
% 0.67/0.90      inference(unit_resolution,[status(thm)],[106, 105])).
% 0.67/0.90  tff(108,plain,
% 0.67/0.90      (iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)),
% 0.67/0.90      inference(and_elim,[status(thm)],[7])).
% 0.67/0.90  tff(109,plain,
% 0.67/0.90      ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))) | (~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))),
% 0.67/0.91      inference(tautology,[status(thm)],[])).
% 0.67/0.91  tff(110,plain,
% 0.67/0.91      ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))),
% 0.67/0.91      inference(unit_resolution,[status(thm)],[109, 108])).
% 0.67/0.91  tff(111,plain,
% 0.67/0.91      (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))),
% 0.67/0.91      inference(unit_resolution,[status(thm)],[110, 107])).
% 0.67/0.91  tff(112,plain,
% 0.67/0.91      (((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))) | ![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))),
% 0.67/0.91      inference(tautology,[status(thm)],[])).
% 0.67/0.91  tff(113,plain,
% 0.67/0.91      (![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))),
% 0.67/0.91      inference(unit_resolution,[status(thm)],[112, 111])).
% 0.67/0.91  tff(114,plain,
% 0.67/0.91      (iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)),
% 0.67/0.91      inference(and_elim,[status(thm)],[7])).
% 0.67/0.91  tff(115,assumption,(~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)), introduced(assumption)).
% 0.67/0.91  tff(116,plain,
% 0.67/0.91      (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))) | ((~iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) | iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))) | (~iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) | iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))),
% 0.67/0.91      inference(rewrite,[status(thm)],[])).
% 0.67/0.91  tff(117,plain,
% 0.67/0.91      ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))) | ((~iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) | iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))),
% 0.67/0.91      inference(quant_inst,[status(thm)],[])).
% 0.67/0.91  tff(118,plain,
% 0.67/0.91      ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))) | (~iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) | iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)),
% 0.67/0.91      inference(modus_ponens,[status(thm)],[117, 116])).
% 0.67/0.91  tff(119,plain,
% 0.67/0.91      ($false),
% 0.67/0.91      inference(unit_resolution,[status(thm)],[118, 115, 114, 113, 91])).
% 0.67/0.91  tff(120,plain,(iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.91  tff(121,plain,
% 0.67/0.91      ((~(~((~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))))) <=> ((~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)))),
% 0.67/0.91      inference(rewrite,[status(thm)],[])).
% 0.67/0.91  tff(122,plain,
% 0.67/0.91      ((iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)) <=> (~((~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))))),
% 0.67/0.91      inference(rewrite,[status(thm)],[])).
% 0.67/0.91  tff(123,plain,
% 0.67/0.91      ((~(iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))) <=> (~(~((~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)))))),
% 0.67/0.91      inference(monotonicity,[status(thm)],[122])).
% 0.67/0.91  tff(124,plain,
% 0.67/0.91      ((~(iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))) <=> ((~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)))),
% 0.67/0.91      inference(transitivity,[status(thm)],[123, 121])).
% 0.67/0.91  tff(125,plain,
% 0.67/0.91      ((~(iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))) <=> (~(iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)))),
% 0.67/0.91      inference(rewrite,[status(thm)],[])).
% 0.67/0.91  tff(126,axiom,(~(iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_025_Cyclic_Dependencies_between_Complex_Properties')).
% 0.67/0.91  tff(127,plain,
% 0.67/0.91      (~(iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))),
% 0.67/0.91      inference(modus_ponens,[status(thm)],[126, 125])).
% 0.67/0.91  tff(128,plain,
% 0.67/0.91      ((~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))),
% 0.67/0.91      inference(modus_ponens,[status(thm)],[127, 124])).
% 0.67/0.91  tff(129,plain,
% 0.67/0.91      (~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)),
% 0.67/0.91      inference(unit_resolution,[status(thm)],[128, 120])).
% 0.67/0.91  tff(130,plain,
% 0.67/0.91      (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | (iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)))),
% 0.67/0.91      inference(rewrite,[status(thm)],[])).
% 0.67/0.91  tff(131,plain,
% 0.67/0.91      (((~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)) <=> (iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)))),
% 0.67/0.91      inference(rewrite,[status(thm)],[])).
% 0.67/0.91  tff(132,plain,
% 0.67/0.91      (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | ((~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | (iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly))))),
% 0.67/0.91      inference(monotonicity,[status(thm)],[131])).
% 0.67/0.91  tff(133,plain,
% 0.67/0.91      (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | ((~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)))),
% 0.67/0.91      inference(transitivity,[status(thm)],[132, 130])).
% 0.67/0.91  tff(134,plain,
% 0.67/0.91      ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | ((~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly))),
% 0.67/0.92      inference(quant_inst,[status(thm)],[])).
% 0.67/0.92  tff(135,plain,
% 0.67/0.92      ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly))),
% 0.67/0.92      inference(modus_ponens,[status(thm)],[134, 133])).
% 0.67/0.92  tff(136,plain,
% 0.67/0.92      ($false),
% 0.67/0.92      inference(unit_resolution,[status(thm)],[135, 129, 53, 52, 51])).
% 0.67/0.92  % SZS output end Proof
% 0.75/0.92  % E exiting
%------------------------------------------------------------------------------