Z3---4.15.1.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : SWB025+2 : TPTP v9.0.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 05:29:40 AM UTC 2025

% Result   : Theorem 0.13s 0.38s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SWB025+2 : TPTP v9.0.0. Released v5.2.0.
% 0.06/0.12  % Command    : run_E %s %d THM
% 0.13/0.33  % Computer : n012.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Fri Jun 20 07:51:25 EDT 2025
% 0.13/0.34  % CPUTime    : 
% 0.13/0.38  % SZS status Theorem
% 0.13/0.38  % SZS output start Proof
% 0.13/0.38  tff(iext_type, type, (
% 0.13/0.38     iext: ( $i * $i * $i ) > $o)).
% 0.13/0.38  tff(uri_ex_hasFather_type, type, (
% 0.13/0.38     uri_ex_hasFather: $i)).
% 0.13/0.38  tff(uri_ex_hasCousin_type, type, (
% 0.13/0.38     uri_ex_hasCousin: $i)).
% 0.13/0.38  tff(uri_ex_hasUncle_type, type, (
% 0.13/0.38     uri_ex_hasUncle: $i)).
% 0.13/0.38  tff(ip_type, type, (
% 0.13/0.38     ip: $i > $o)).
% 0.13/0.38  tff(tptp_fun_BNODE_l11_9_type, type, (
% 0.13/0.38     tptp_fun_BNODE_l11_9: $i)).
% 0.13/0.38  tff(uri_owl_propertyChainAxiom_type, type, (
% 0.13/0.38     uri_owl_propertyChainAxiom: $i)).
% 0.13/0.38  tff(tptp_fun_Y2_0_type, type, (
% 0.13/0.38     tptp_fun_Y2_0: ( $i * $i * $i ) > $i)).
% 0.13/0.38  tff(tptp_fun_Y0_2_type, type, (
% 0.13/0.38     tptp_fun_Y0_2: ( $i * $i * $i ) > $i)).
% 0.13/0.38  tff(tptp_fun_Y1_1_type, type, (
% 0.13/0.38     tptp_fun_Y1_1: ( $i * $i * $i ) > $i)).
% 0.13/0.38  tff(uri_rdf_nil_type, type, (
% 0.13/0.38     uri_rdf_nil: $i)).
% 0.13/0.38  tff(tptp_fun_BNODE_l12_8_type, type, (
% 0.13/0.38     tptp_fun_BNODE_l12_8: $i)).
% 0.13/0.38  tff(uri_rdf_rest_type, type, (
% 0.13/0.38     uri_rdf_rest: $i)).
% 0.13/0.38  tff(uri_ex_dave_type, type, (
% 0.13/0.38     uri_ex_dave: $i)).
% 0.13/0.38  tff(uri_ex_bob_type, type, (
% 0.13/0.38     uri_ex_bob: $i)).
% 0.13/0.38  tff(uri_ex_charly_type, type, (
% 0.13/0.38     uri_ex_charly: $i)).
% 0.13/0.38  tff(uri_ex_alice_type, type, (
% 0.13/0.38     uri_ex_alice: $i)).
% 0.13/0.38  tff(tptp_fun_BNODE_l3_5_type, type, (
% 0.13/0.38     tptp_fun_BNODE_l3_5: $i)).
% 0.13/0.38  tff(uri_owl_inverseOf_type, type, (
% 0.13/0.38     uri_owl_inverseOf: $i)).
% 0.13/0.38  tff(tptp_fun_BNODE_l22_6_type, type, (
% 0.13/0.38     tptp_fun_BNODE_l22_6: $i)).
% 0.13/0.38  tff(uri_rdf_first_type, type, (
% 0.13/0.38     uri_rdf_first: $i)).
% 0.13/0.38  tff(tptp_fun_BNODE_l21_7_type, type, (
% 0.13/0.38     tptp_fun_BNODE_l21_7: $i)).
% 0.13/0.38  tff(tptp_fun_X_4_type, type, (
% 0.13/0.38     tptp_fun_X_4: ( $i * $i ) > $i)).
% 0.13/0.38  tff(tptp_fun_Y_3_type, type, (
% 0.13/0.38     tptp_fun_Y_3: ( $i * $i ) > $i)).
% 0.13/0.38  tff(1,plain,
% 0.13/0.38      (?[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))),
% 0.13/0.38      inference(rewrite,[status(thm)],[])).
% 0.13/0.38  tff(2,plain,
% 0.13/0.38      (^[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))))),
% 0.21/0.40      inference(bind,[status(th)],[])).
% 0.21/0.40  tff(3,plain,
% 0.21/0.40      (?[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))),
% 0.21/0.40      inference(quant_intro,[status(thm)],[2])).
% 0.21/0.40  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/sandbox/benchmark/theBenchmark.p','testcase_premise_fullish_025_Cyclic_Dependencies_between_Complex_Properties')).
% 0.21/0.40  tff(5,plain,
% 0.21/0.40      (?[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))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.40  tff(6,plain,
% 0.21/0.40      (?[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))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.40  tff(7,plain,(
% 0.21/0.40      iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) & iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8) & iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) & iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6) & iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5) & iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3!5, 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)),
% 0.21/0.40      inference(skolemize,[status(sab)],[6])).
% 0.21/0.40  tff(8,plain,
% 0.21/0.40      (iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)),
% 0.21/0.40      inference(and_elim,[status(thm)],[7])).
% 0.21/0.40  tff(9,plain,
% 0.21/0.40      (iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)),
% 0.21/0.40      inference(and_elim,[status(thm)],[7])).
% 0.21/0.41  tff(10,plain,
% 0.21/0.41      (iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)),
% 0.21/0.41      inference(and_elim,[status(thm)],[7])).
% 0.21/0.41  tff(11,plain,
% 0.21/0.41      (iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)),
% 0.21/0.41      inference(and_elim,[status(thm)],[7])).
% 0.21/0.41  tff(12,plain,
% 0.21/0.41      (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, 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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, 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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, 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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, 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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))))),
% 0.21/0.41      inference(bind,[status(th)],[])).
% 0.21/0.41  tff(13,plain,
% 0.21/0.41      (![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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))),
% 0.21/0.41      inference(quant_intro,[status(thm)],[12])).
% 0.21/0.41  tff(14,plain,
% 0.21/0.41      (^[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(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))))),
% 0.21/0.41      inference(bind,[status(th)],[])).
% 0.21/0.41  tff(15,plain,
% 0.21/0.41      (![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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.21/0.41      inference(quant_intro,[status(thm)],[14])).
% 0.21/0.41  tff(16,plain,
% 0.21/0.41      (^[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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))))),
% 0.21/0.41      inference(bind,[status(th)],[])).
% 0.21/0.41  tff(17,plain,
% 0.21/0.41      (![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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.21/0.41      inference(quant_intro,[status(thm)],[16])).
% 0.21/0.41  tff(18,plain,
% 0.21/0.41      (![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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.21/0.41      inference(transitivity,[status(thm)],[17, 15])).
% 0.21/0.41  tff(19,plain,
% 0.21/0.41      (^[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(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))), trans(monotonicity(rewrite((~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) <=> (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))) <=> (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))), rewrite((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))))),
% 0.21/0.42      inference(bind,[status(th)],[])).
% 0.21/0.42  tff(20,plain,
% 0.21/0.42      (![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_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.21/0.42      inference(quant_intro,[status(thm)],[19])).
% 0.21/0.42  tff(21,plain,
% 0.21/0.42      (^[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_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))),
% 0.21/0.42      inference(bind,[status(th)],[])).
% 0.21/0.42  tff(22,plain,
% 0.21/0.42      (![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_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))),
% 0.21/0.42      inference(quant_intro,[status(thm)],[21])).
% 0.21/0.42  tff(23,plain,
% 0.21/0.42      (![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)))))),
% 0.21/0.42      inference(rewrite,[status(thm)],[])).
% 0.21/0.42  tff(24,plain,
% 0.21/0.42      (^[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)))))))),
% 0.21/0.42      inference(bind,[status(th)],[])).
% 0.21/0.42  tff(25,plain,
% 0.21/0.42      (![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)))))),
% 0.21/0.42      inference(quant_intro,[status(thm)],[24])).
% 0.21/0.42  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/sandbox/benchmark/theBenchmark.p','owl_chain_002')).
% 0.21/0.42  tff(27,plain,
% 0.21/0.42      (![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)))))),
% 0.21/0.42      inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.42  tff(28,plain,
% 0.21/0.42      (![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)))))),
% 0.21/0.42      inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.42  tff(29,plain,(
% 0.21/0.42      ![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_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))),
% 0.21/0.42      inference(skolemize,[status(sab)],[28])).
% 0.21/0.42  tff(30,plain,
% 0.21/0.42      (![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_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))),
% 0.21/0.42      inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.42  tff(31,plain,
% 0.21/0.42      (![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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.21/0.42      inference(modus_ponens,[status(thm)],[30, 20])).
% 0.21/0.42  tff(32,plain,
% 0.21/0.42      (![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(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.21/0.42      inference(modus_ponens,[status(thm)],[31, 18])).
% 0.21/0.42  tff(33,plain,
% 0.21/0.42      (![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))),
% 0.21/0.43      inference(modus_ponens,[status(thm)],[32, 13])).
% 0.21/0.43  tff(34,plain,
% 0.21/0.43      (((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)))))))))) <=> ((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)))))))))),
% 0.21/0.43      inference(rewrite,[status(thm)],[])).
% 0.21/0.43  tff(35,plain,
% 0.21/0.43      (((~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle))))))))) <=> ((~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)))))))))),
% 0.21/0.43      inference(rewrite,[status(thm)],[])).
% 0.21/0.43  tff(36,plain,
% 0.21/0.43      ((~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle))))))))),
% 0.21/0.43      inference(rewrite,[status(thm)],[])).
% 0.21/0.43  tff(37,plain,
% 0.21/0.43      (((~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)))))))))),
% 0.21/0.43      inference(monotonicity,[status(thm)],[36])).
% 0.21/0.43  tff(38,plain,
% 0.21/0.43      (((~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2))))))))))) <=> ((~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)))))))))),
% 0.21/0.43      inference(transitivity,[status(thm)],[37, 35])).
% 0.21/0.43  tff(39,plain,
% 0.21/0.43      (((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, 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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle))))))))))),
% 0.21/0.44      inference(monotonicity,[status(thm)],[38])).
% 0.21/0.44  tff(40,plain,
% 0.21/0.44      (((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, 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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)))))))))),
% 0.21/0.44      inference(transitivity,[status(thm)],[39, 34])).
% 0.21/0.44  tff(41,plain,
% 0.21/0.44      ((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasFather)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))))))))))),
% 0.21/0.44      inference(quant_inst,[status(thm)],[])).
% 0.21/0.44  tff(42,plain,
% 0.21/0.44      ((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle))))))))),
% 0.21/0.44      inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.44  tff(43,plain,
% 0.21/0.44      (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)))))))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[42, 33, 11, 10, 9, 8])).
% 0.21/0.44  tff(44,plain,
% 0.21/0.44      (((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~((~iext(uri_ex_hasFather, tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_1(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | iext(uri_ex_hasUncle, tptp_fun_Y0_2(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_0(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle))))))) | ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)))))),
% 0.21/0.44      inference(tautology,[status(thm)],[])).
% 0.21/0.44  tff(45,plain,
% 0.21/0.44      ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle))))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[44, 43])).
% 0.21/0.44  tff(46,plain,
% 0.21/0.44      (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)),
% 0.21/0.44      inference(and_elim,[status(thm)],[7])).
% 0.21/0.44  tff(47,plain,
% 0.21/0.44      ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)))))) | (~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle))))),
% 0.21/0.44      inference(tautology,[status(thm)],[])).
% 0.21/0.44  tff(48,plain,
% 0.21/0.44      ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~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_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle))))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[47, 46])).
% 0.21/0.44  tff(49,plain,
% 0.21/0.44      (~((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)))),
% 0.21/0.44      inference(unit_resolution,[status(thm)],[48, 45])).
% 0.21/0.44  tff(50,plain,
% 0.21/0.44      (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (~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_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))),
% 0.21/0.44      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(51,plain,
% 0.21/0.45      (![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[50, 49])).
% 0.21/0.45  tff(52,plain,
% 0.21/0.45      (iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)),
% 0.21/0.45      inference(and_elim,[status(thm)],[7])).
% 0.21/0.45  tff(53,plain,
% 0.21/0.45      (iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)),
% 0.21/0.45      inference(and_elim,[status(thm)],[7])).
% 0.21/0.45  tff(54,plain,
% 0.21/0.45      (^[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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1)))))))) <=> (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))))))),
% 0.21/0.45      inference(bind,[status(th)],[])).
% 0.21/0.45  tff(55,plain,
% 0.21/0.45      (![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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[54])).
% 0.21/0.45  tff(56,plain,
% 0.21/0.45      (^[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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1)))))))))),
% 0.21/0.45      inference(bind,[status(th)],[])).
% 0.21/0.45  tff(57,plain,
% 0.21/0.45      (![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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))))))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[56])).
% 0.21/0.45  tff(58,plain,
% 0.21/0.45      (^[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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1)))))))))),
% 0.21/0.45      inference(bind,[status(th)],[])).
% 0.21/0.45  tff(59,plain,
% 0.21/0.45      (![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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))))))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[58])).
% 0.21/0.45  tff(60,plain,
% 0.21/0.45      (![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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))))))),
% 0.21/0.45      inference(transitivity,[status(thm)],[59, 57])).
% 0.21/0.45  tff(61,plain,
% 0.21/0.45      (^[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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1)))) <=> (~(iext(P1, tptp_fun_X_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))), ((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))))), rewrite((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1)))))), ((iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))))))))),
% 0.21/0.45      inference(bind,[status(th)],[])).
% 0.21/0.45  tff(62,plain,
% 0.21/0.45      (![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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))))))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[61])).
% 0.21/0.45  tff(63,plain,
% 0.21/0.45      (^[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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1)))))))),
% 0.21/0.45      inference(bind,[status(th)],[])).
% 0.21/0.45  tff(64,plain,
% 0.21/0.45      (![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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[63])).
% 0.21/0.45  tff(65,plain,
% 0.21/0.45      (![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))))),
% 0.21/0.45      inference(rewrite,[status(thm)],[])).
% 0.21/0.45  tff(66,plain,
% 0.21/0.45      (^[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)))))),
% 0.21/0.45      inference(bind,[status(th)],[])).
% 0.21/0.45  tff(67,plain,
% 0.21/0.45      (![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))))),
% 0.21/0.45      inference(quant_intro,[status(thm)],[66])).
% 0.21/0.45  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/sandbox/benchmark/theBenchmark.p','owl_inv')).
% 0.21/0.45  tff(69,plain,
% 0.21/0.45      (![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))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.45  tff(70,plain,
% 0.21/0.45      (![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))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.45  tff(71,plain,(
% 0.21/0.45      ![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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1)))))))),
% 0.21/0.45      inference(skolemize,[status(sab)],[70])).
% 0.21/0.45  tff(72,plain,
% 0.21/0.45      (![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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[71, 64])).
% 0.21/0.45  tff(73,plain,
% 0.21/0.45      (![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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[72, 62])).
% 0.21/0.45  tff(74,plain,
% 0.21/0.45      (![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_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1))))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[73, 60])).
% 0.21/0.45  tff(75,plain,
% 0.21/0.45      (![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(P2, P1)))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.21/0.45      inference(modus_ponens,[status(thm)],[74, 55])).
% 0.21/0.45  tff(76,plain,
% 0.21/0.45      ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~(iext(P1, tptp_fun_X_4(P2, P1), tptp_fun_Y_3(P2, P1)) <=> iext(P2, tptp_fun_Y_3(P2, P1), tptp_fun_X_4(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!5, uri_ex_hasFather) | (~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~(iext(BNODE_l3!5, tptp_fun_X_4(uri_ex_hasFather, BNODE_l3!5), tptp_fun_Y_3(uri_ex_hasFather, BNODE_l3!5)) <=> iext(uri_ex_hasFather, tptp_fun_Y_3(uri_ex_hasFather, BNODE_l3!5), tptp_fun_X_4(uri_ex_hasFather, BNODE_l3!5)))))) | (~((~iext(uri_owl_inverseOf, BNODE_l3!5, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))))))),
% 0.21/0.45      inference(quant_inst,[status(thm)],[])).
% 0.21/0.45  tff(77,plain,
% 0.21/0.45      (~((~(iext(uri_owl_inverseOf, BNODE_l3!5, uri_ex_hasFather) | (~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~(iext(BNODE_l3!5, tptp_fun_X_4(uri_ex_hasFather, BNODE_l3!5), tptp_fun_Y_3(uri_ex_hasFather, BNODE_l3!5)) <=> iext(uri_ex_hasFather, tptp_fun_Y_3(uri_ex_hasFather, BNODE_l3!5), tptp_fun_X_4(uri_ex_hasFather, BNODE_l3!5)))))) | (~((~iext(uri_owl_inverseOf, BNODE_l3!5, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X))))))))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.45  tff(78,plain,
% 0.21/0.45      (((~(iext(uri_owl_inverseOf, BNODE_l3!5, uri_ex_hasFather) | (~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~(iext(BNODE_l3!5, tptp_fun_X_4(uri_ex_hasFather, BNODE_l3!5), tptp_fun_Y_3(uri_ex_hasFather, BNODE_l3!5)) <=> iext(uri_ex_hasFather, tptp_fun_Y_3(uri_ex_hasFather, BNODE_l3!5), tptp_fun_X_4(uri_ex_hasFather, BNODE_l3!5)))))) | (~((~iext(uri_owl_inverseOf, BNODE_l3!5, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))))) | ((~iext(uri_owl_inverseOf, BNODE_l3!5, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X))))))),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(79,plain,
% 0.21/0.45      ((~iext(uri_owl_inverseOf, BNODE_l3!5, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[78, 77])).
% 0.21/0.45  tff(80,plain,
% 0.21/0.45      (iext(uri_owl_inverseOf, BNODE_l3!5, uri_ex_hasFather)),
% 0.21/0.45      inference(and_elim,[status(thm)],[7])).
% 0.21/0.45  tff(81,plain,
% 0.21/0.45      ((~((~iext(uri_owl_inverseOf, BNODE_l3!5, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X))))))) | (~iext(uri_owl_inverseOf, BNODE_l3!5, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(82,plain,
% 0.21/0.45      ((~((~iext(uri_owl_inverseOf, BNODE_l3!5, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X))))))) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[81, 80])).
% 0.21/0.45  tff(83,plain,
% 0.21/0.45      (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X))))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[82, 79])).
% 0.21/0.45  tff(84,plain,
% 0.21/0.45      (((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X)))) | ![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X))),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(85,plain,
% 0.21/0.45      (![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X))),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[84, 83])).
% 0.21/0.45  tff(86,plain,
% 0.21/0.45      ((~![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X))) | (iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))),
% 0.21/0.45      inference(quant_inst,[status(thm)],[])).
% 0.21/0.45  tff(87,plain,
% 0.21/0.45      (iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[86, 85])).
% 0.21/0.45  tff(88,plain,
% 0.21/0.45      (iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)),
% 0.21/0.45      inference(and_elim,[status(thm)],[7])).
% 0.21/0.45  tff(89,plain,
% 0.21/0.45      ((~(iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))) | iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice) | (~iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))),
% 0.21/0.45      inference(tautology,[status(thm)],[])).
% 0.21/0.45  tff(90,plain,
% 0.21/0.45      ((~(iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))) | iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice)),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[89, 88])).
% 0.21/0.45  tff(91,plain,
% 0.21/0.45      (iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice)),
% 0.21/0.45      inference(unit_resolution,[status(thm)],[90, 87])).
% 0.21/0.45  tff(92,plain,
% 0.21/0.45      (iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)),
% 0.21/0.45      inference(and_elim,[status(thm)],[7])).
% 0.21/0.45  tff(93,plain,
% 0.21/0.45      (iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)),
% 0.21/0.45      inference(and_elim,[status(thm)],[7])).
% 0.21/0.45  tff(94,plain,
% 0.21/0.45      (iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)),
% 0.21/0.45      inference(and_elim,[status(thm)],[7])).
% 0.21/0.46  tff(95,plain,
% 0.21/0.46      (iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)),
% 0.21/0.46      inference(and_elim,[status(thm)],[7])).
% 0.21/0.46  tff(96,plain,
% 0.21/0.46      (((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~((~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5)))))))))) <=> ((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~((~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5)))))))))),
% 0.21/0.46      inference(rewrite,[status(thm)],[])).
% 0.21/0.46  tff(97,plain,
% 0.21/0.46      (((~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~((~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5))))))))) <=> ((~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~((~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5)))))))))),
% 0.21/0.46      inference(rewrite,[status(thm)],[])).
% 0.21/0.46  tff(98,plain,
% 0.21/0.46      ((~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~((~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5))))))))),
% 0.21/0.46      inference(rewrite,[status(thm)],[])).
% 0.21/0.46  tff(99,plain,
% 0.21/0.46      (((~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~((~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5)))))))))),
% 0.21/0.46      inference(monotonicity,[status(thm)],[98])).
% 0.21/0.46  tff(100,plain,
% 0.21/0.46      (((~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2))))))))))) <=> ((~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~((~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5)))))))))),
% 0.21/0.46      inference(transitivity,[status(thm)],[99, 97])).
% 0.21/0.46  tff(101,plain,
% 0.21/0.46      (((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, 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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~((~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5))))))))))),
% 0.21/0.46      inference(monotonicity,[status(thm)],[100])).
% 0.21/0.46  tff(102,plain,
% 0.21/0.46      (((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, 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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~((~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5)))))))))),
% 0.21/0.47      inference(transitivity,[status(thm)],[101, 96])).
% 0.21/0.47  tff(103,plain,
% 0.21/0.47      ((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))))))))))),
% 0.21/0.47      inference(quant_inst,[status(thm)],[])).
% 0.21/0.47  tff(104,plain,
% 0.21/0.47      ((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P1, Y0, Y1)) | (~iext(P2, Y1, Y2)))))))))))) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~((~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5))))))))),
% 0.21/0.47      inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.47  tff(105,plain,
% 0.21/0.47      (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~((~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5)))))))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[104, 33, 95, 94, 93, 92])).
% 0.21/0.47  tff(106,plain,
% 0.21/0.47      (((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~((~iext(BNODE_l3!5, tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_1(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin))) | iext(uri_ex_hasCousin, tptp_fun_Y0_2(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_0(BNODE_l3!5, uri_ex_hasUncle, uri_ex_hasCousin)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5))))))) | ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5)))))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(107,plain,
% 0.21/0.47      ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5))))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[106, 105])).
% 0.21/0.47  tff(108,plain,
% 0.21/0.47      (iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)),
% 0.21/0.47      inference(and_elim,[status(thm)],[7])).
% 0.21/0.47  tff(109,plain,
% 0.21/0.47      ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5)))))) | (~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5))))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(110,plain,
% 0.21/0.47      ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5)))))) | (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5))))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[109, 108])).
% 0.21/0.47  tff(111,plain,
% 0.21/0.47      (~((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5)))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[110, 107])).
% 0.21/0.47  tff(112,plain,
% 0.21/0.47      (((~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (~ip(BNODE_l3!5))) | ![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))),
% 0.21/0.47      inference(tautology,[status(thm)],[])).
% 0.21/0.47  tff(113,plain,
% 0.21/0.47      (![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[112, 111])).
% 0.21/0.47  tff(114,plain,
% 0.21/0.47      (iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)),
% 0.21/0.47      inference(and_elim,[status(thm)],[7])).
% 0.21/0.47  tff(115,assumption,(~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)), introduced(assumption)).
% 0.21/0.47  tff(116,plain,
% 0.21/0.47      (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice) | (~iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice) | (~iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(117,plain,
% 0.21/0.47      ((iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) | (~iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice))) <=> (iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice) | (~iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(118,plain,
% 0.21/0.47      (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) | (~iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice) | (~iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave))))),
% 0.21/0.47      inference(monotonicity,[status(thm)],[117])).
% 0.21/0.47  tff(119,plain,
% 0.21/0.47      (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) | (~iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice) | (~iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)))),
% 0.21/0.47      inference(transitivity,[status(thm)],[118, 116])).
% 0.21/0.47  tff(120,plain,
% 0.21/0.47      ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | (iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) | (~iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice)))),
% 0.21/0.47      inference(quant_inst,[status(thm)],[])).
% 0.21/0.47  tff(121,plain,
% 0.21/0.47      ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice) | (~iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave))),
% 0.21/0.47      inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.47  tff(122,plain,
% 0.21/0.47      ($false),
% 0.21/0.47      inference(unit_resolution,[status(thm)],[121, 115, 114, 113, 91])).
% 0.21/0.47  tff(123,plain,(iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47  tff(124,plain,
% 0.21/0.47      ((~(~((~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)))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(125,plain,
% 0.21/0.47      ((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))))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(126,plain,
% 0.21/0.47      ((~(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)))))),
% 0.21/0.47      inference(monotonicity,[status(thm)],[125])).
% 0.21/0.47  tff(127,plain,
% 0.21/0.47      ((~(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)))),
% 0.21/0.47      inference(transitivity,[status(thm)],[126, 124])).
% 0.21/0.47  tff(128,plain,
% 0.21/0.47      ((~(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)))),
% 0.21/0.47      inference(rewrite,[status(thm)],[])).
% 0.21/0.47  tff(129,axiom,(~(iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_conclusion_fullish_025_Cyclic_Dependencies_between_Complex_Properties')).
% 0.21/0.48  tff(130,plain,
% 0.21/0.48      (~(iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))),
% 0.21/0.48      inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.48  tff(131,plain,
% 0.21/0.48      ((~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))),
% 0.21/0.48      inference(modus_ponens,[status(thm)],[130, 127])).
% 0.21/0.48  tff(132,plain,
% 0.21/0.48      (~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[131, 123])).
% 0.21/0.48  tff(133,plain,
% 0.21/0.48      (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)))),
% 0.21/0.48      inference(rewrite,[status(thm)],[])).
% 0.21/0.48  tff(134,plain,
% 0.21/0.48      ((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))) <=> (iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)))),
% 0.21/0.48      inference(rewrite,[status(thm)],[])).
% 0.21/0.48  tff(135,plain,
% 0.21/0.48      (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, 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_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | (iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob))))),
% 0.21/0.48      inference(monotonicity,[status(thm)],[134])).
% 0.21/0.48  tff(136,plain,
% 0.21/0.48      (((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, 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_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)))),
% 0.21/0.48      inference(transitivity,[status(thm)],[135, 133])).
% 0.21/0.48  tff(137,plain,
% 0.21/0.48      ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, 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)))),
% 0.21/0.48      inference(quant_inst,[status(thm)],[])).
% 0.21/0.48  tff(138,plain,
% 0.21/0.48      ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob))),
% 0.21/0.48      inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.48  tff(139,plain,
% 0.21/0.48      ($false),
% 0.21/0.48      inference(unit_resolution,[status(thm)],[138, 132, 53, 52, 51])).
% 0.21/0.48  % SZS output end Proof
% 0.21/0.48  % E exiting
%------------------------------------------------------------------------------