TSTP Solution File: SWB025+2 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB025+2 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 08:31:56 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWB025+2 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 20:01:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(iext_type, type, (
% 0.19/0.39 iext: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(uri_ex_hasFather_type, type, (
% 0.19/0.39 uri_ex_hasFather: $i)).
% 0.19/0.39 tff(uri_ex_hasCousin_type, type, (
% 0.19/0.39 uri_ex_hasCousin: $i)).
% 0.19/0.39 tff(uri_ex_hasUncle_type, type, (
% 0.19/0.39 uri_ex_hasUncle: $i)).
% 0.19/0.39 tff(ip_type, type, (
% 0.19/0.39 ip: $i > $o)).
% 0.19/0.39 tff(tptp_fun_BNODE_l11_9_type, type, (
% 0.19/0.39 tptp_fun_BNODE_l11_9: $i)).
% 0.19/0.39 tff(uri_owl_propertyChainAxiom_type, type, (
% 0.19/0.39 uri_owl_propertyChainAxiom: $i)).
% 0.19/0.39 tff(tptp_fun_Y1_1_type, type, (
% 0.19/0.39 tptp_fun_Y1_1: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Y0_2_type, type, (
% 0.19/0.39 tptp_fun_Y0_2: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Y2_0_type, type, (
% 0.19/0.39 tptp_fun_Y2_0: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(uri_rdf_nil_type, type, (
% 0.19/0.39 uri_rdf_nil: $i)).
% 0.19/0.39 tff(tptp_fun_BNODE_l12_8_type, type, (
% 0.19/0.39 tptp_fun_BNODE_l12_8: $i)).
% 0.19/0.39 tff(uri_rdf_rest_type, type, (
% 0.19/0.39 uri_rdf_rest: $i)).
% 0.19/0.39 tff(uri_ex_dave_type, type, (
% 0.19/0.39 uri_ex_dave: $i)).
% 0.19/0.39 tff(uri_ex_bob_type, type, (
% 0.19/0.39 uri_ex_bob: $i)).
% 0.19/0.39 tff(uri_ex_charly_type, type, (
% 0.19/0.39 uri_ex_charly: $i)).
% 0.19/0.39 tff(uri_ex_alice_type, type, (
% 0.19/0.39 uri_ex_alice: $i)).
% 0.19/0.39 tff(tptp_fun_BNODE_l3_5_type, type, (
% 0.19/0.39 tptp_fun_BNODE_l3_5: $i)).
% 0.19/0.39 tff(uri_owl_inverseOf_type, type, (
% 0.19/0.39 uri_owl_inverseOf: $i)).
% 0.19/0.39 tff(tptp_fun_BNODE_l22_6_type, type, (
% 0.19/0.39 tptp_fun_BNODE_l22_6: $i)).
% 0.19/0.39 tff(uri_rdf_first_type, type, (
% 0.19/0.39 uri_rdf_first: $i)).
% 0.19/0.39 tff(tptp_fun_BNODE_l21_7_type, type, (
% 0.19/0.39 tptp_fun_BNODE_l21_7: $i)).
% 0.19/0.39 tff(tptp_fun_X_4_type, type, (
% 0.19/0.39 tptp_fun_X_4: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.39 tptp_fun_Y_3: ( $i * $i ) > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (?[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))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (?[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))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.41 tff(4,axiom,(?[BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l3: $i] : ((((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, BNODE_l3)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l3, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_premise_fullish_025_Cyclic_Dependencies_between_Complex_Properties')).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (?[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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (?[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))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.41 tff(7,plain,(
% 0.19/0.41 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)),
% 0.19/0.41 inference(skolemize,[status(sab)],[6])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)),
% 0.19/0.41 inference(and_elim,[status(thm)],[7])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (iext(uri_rdf_first, BNODE_l12!8, uri_ex_hasFather)),
% 0.19/0.41 inference(and_elim,[status(thm)],[7])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)),
% 0.19/0.42 inference(and_elim,[status(thm)],[7])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (iext(uri_rdf_first, BNODE_l11!9, uri_ex_hasCousin)),
% 0.19/0.42 inference(and_elim,[status(thm)],[7])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (^[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)))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 (![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)))))))))) <=> ![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)))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 (^[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)))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (![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)))))))))) <=> ![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))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 (^[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(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)))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(17,plain,
% 0.19/0.42 (![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)))))))))) <=> ![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))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.42 tff(18,plain,
% 0.19/0.42 (![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)))))))))) <=> ![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))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.42 tff(19,plain,
% 0.19/0.42 (^[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_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))))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (![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) & ![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))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (^[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))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (![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) & ![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)))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (![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) & ![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)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (^[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)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (![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)) & ![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)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.43 tff(26,axiom,(![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_chain_002')).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 (![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) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 (![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) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.43 tff(29,plain,(
% 0.19/0.43 ![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) & ![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))))))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[28])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 (![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) & ![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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 (![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)) | (~![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))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (![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)) | (~![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))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[31, 18])).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 (![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)))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[32, 13])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 (((~![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_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(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_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_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![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_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_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(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_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_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 (((~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_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(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_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_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![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_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(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_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_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 ((~((~(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_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(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_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_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2))))))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 (((~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_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(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_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_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))))))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (((~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_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(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_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_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[37, 35])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (((~![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_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_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(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_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_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2))))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[38])).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 (((~![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_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_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(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_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_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[39, 34])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 ((~![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)))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 ((~![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_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(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_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_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(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_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_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[42, 33, 11, 10, 9, 8])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 (((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(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_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_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![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_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)),
% 0.19/0.45 inference(and_elim,[status(thm)],[7])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![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_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!9)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![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_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 (((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2))))) | ![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(51,plain,
% 0.19/0.46 (![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.46 tff(52,plain,
% 0.19/0.46 (iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)),
% 0.19/0.46 inference(and_elim,[status(thm)],[7])).
% 0.19/0.46 tff(53,plain,
% 0.19/0.46 (iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)),
% 0.19/0.46 inference(and_elim,[status(thm)],[7])).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 (^[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))))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(55,plain,
% 0.19/0.46 (![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)))))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.46 tff(56,plain,
% 0.19/0.46 (^[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))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(57,plain,
% 0.19/0.46 (![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)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 (^[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))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 (![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)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 (![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)))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[59, 57])).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 (^[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))))))), 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(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)))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(62,plain,
% 0.19/0.46 (![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)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.46 tff(63,plain,
% 0.19/0.46 (^[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))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (![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)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(66,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(67,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.46 tff(68,axiom,(![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_inv')).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.46 tff(70,plain,
% 0.19/0.46 (![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))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.19/0.46 tff(71,plain,(
% 0.19/0.46 ![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)))))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[70])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 (![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.19/0.46 tff(73,plain,
% 0.19/0.46 (![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)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 (![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)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[73, 60])).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 (![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)))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[74, 55])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 ((~![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)))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 (~((~(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))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 (((~(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))))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 ((~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)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 (iext(uri_owl_inverseOf, BNODE_l3!5, uri_ex_hasFather)),
% 0.19/0.47 inference(and_elim,[status(thm)],[7])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 ((~((~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)))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 ((~((~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)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!5)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 (((~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))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(85,plain,
% 0.19/0.47 (![X: $i, Y: $i] : (iext(BNODE_l3!5, X, Y) <=> iext(uri_ex_hasFather, Y, X))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.47 tff(86,plain,
% 0.19/0.47 ((~![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))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(87,plain,
% 0.19/0.47 (iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.47 tff(88,plain,
% 0.19/0.47 (iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)),
% 0.19/0.47 inference(and_elim,[status(thm)],[7])).
% 0.19/0.47 tff(89,plain,
% 0.19/0.47 ((~(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))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(90,plain,
% 0.19/0.47 ((~(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)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.19/0.47 tff(91,plain,
% 0.19/0.47 (iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[90, 87])).
% 0.19/0.47 tff(92,plain,
% 0.19/0.47 (iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)),
% 0.19/0.47 inference(and_elim,[status(thm)],[7])).
% 0.19/0.47 tff(93,plain,
% 0.19/0.47 (iext(uri_rdf_first, BNODE_l22!6, BNODE_l3!5)),
% 0.19/0.47 inference(and_elim,[status(thm)],[7])).
% 0.19/0.47 tff(94,plain,
% 0.19/0.47 (iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)),
% 0.19/0.47 inference(and_elim,[status(thm)],[7])).
% 0.19/0.47 tff(95,plain,
% 0.19/0.47 (iext(uri_rdf_first, BNODE_l21!7, uri_ex_hasUncle)),
% 0.19/0.47 inference(and_elim,[status(thm)],[7])).
% 0.19/0.47 tff(96,plain,
% 0.19/0.47 (((~![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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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)))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(97,plain,
% 0.19/0.47 (((~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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)))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(98,plain,
% 0.19/0.47 ((~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~ip(BNODE_l3!5)) | (~(iext(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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(99,plain,
% 0.19/0.47 (((~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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)))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[98])).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 (((~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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)))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[99, 97])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 (((~![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_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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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))))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[100])).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 (((~![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_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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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)))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[101, 96])).
% 0.19/0.48 tff(103,plain,
% 0.19/0.48 ((~![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)))))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(104,plain,
% 0.19/0.48 ((~![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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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))))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.48 tff(105,plain,
% 0.19/0.48 (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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)))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[104, 33, 95, 94, 93, 92])).
% 0.19/0.48 tff(106,plain,
% 0.19/0.48 (((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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)))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 (iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)),
% 0.19/0.49 inference(and_elim,[status(thm)],[7])).
% 0.19/0.49 tff(109,plain,
% 0.19/0.49 ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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))))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(110,plain,
% 0.19/0.49 ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!7)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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)))))))) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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))))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.19/0.49 tff(111,plain,
% 0.19/0.49 (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[110, 107])).
% 0.19/0.49 tff(112,plain,
% 0.19/0.49 (((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~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))))) | ![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(113,plain,
% 0.19/0.49 (![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.19/0.49 tff(114,plain,
% 0.19/0.49 (iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)),
% 0.19/0.49 inference(and_elim,[status(thm)],[7])).
% 0.19/0.49 tff(115,assumption,(~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)), introduced(assumption)).
% 0.19/0.49 tff(116,plain,
% 0.19/0.49 (((~![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(117,plain,
% 0.19/0.49 ((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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(118,plain,
% 0.19/0.49 (((~![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))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.49 tff(119,plain,
% 0.19/0.49 (((~![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)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[118, 116])).
% 0.19/0.49 tff(120,plain,
% 0.19/0.49 ((~![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)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(121,plain,
% 0.19/0.49 ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(uri_ex_hasUncle, Y0, Y1)) | (~iext(BNODE_l3!5, Y1, Y2)))) | iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice) | (~iext(BNODE_l3!5, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.49 tff(122,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[121, 115, 114, 113, 91])).
% 0.19/0.49 tff(123,plain,(iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(124,plain,
% 0.19/0.49 ((~(~((~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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(125,plain,
% 0.19/0.49 ((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))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(126,plain,
% 0.19/0.49 ((~(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)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[125])).
% 0.19/0.49 tff(127,plain,
% 0.19/0.49 ((~(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)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[126, 124])).
% 0.19/0.49 tff(128,plain,
% 0.19/0.49 ((~(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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 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/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_025_Cyclic_Dependencies_between_Complex_Properties')).
% 0.19/0.49 tff(130,plain,
% 0.19/0.49 (~(iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.49 tff(131,plain,
% 0.19/0.49 ((~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[130, 127])).
% 0.19/0.49 tff(132,plain,
% 0.19/0.49 (~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[131, 123])).
% 0.19/0.49 tff(133,plain,
% 0.19/0.49 (((~![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(134,plain,
% 0.19/0.49 ((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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(135,plain,
% 0.19/0.49 (((~![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))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[134])).
% 0.19/0.49 tff(136,plain,
% 0.19/0.49 (((~![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)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[135, 133])).
% 0.19/0.49 tff(137,plain,
% 0.19/0.49 ((~![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)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(138,plain,
% 0.19/0.49 ((~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasCousin, Y0, Y1)) | (~iext(uri_ex_hasFather, Y1, Y2)))) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.49 tff(139,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[138, 132, 53, 52, 51])).
% 0.19/0.49 % SZS output end Proof
%------------------------------------------------------------------------------