TSTP Solution File: SWB025+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB025+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 08:31:56 EDT 2022
% Result : Theorem 0.80s 0.78s
% Output : Proof 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWB025+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 19:43:20 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.
% 0.80/0.78 % SZS status Theorem
% 0.80/0.78 % SZS output start Proof
% 0.80/0.78 tff(iext_type, type, (
% 0.80/0.78 iext: ( $i * $i * $i ) > $o)).
% 0.80/0.78 tff(uri_ex_hasUncle_type, type, (
% 0.80/0.78 uri_ex_hasUncle: $i)).
% 0.80/0.78 tff(uri_ex_hasCousin_type, type, (
% 0.80/0.78 uri_ex_hasCousin: $i)).
% 0.80/0.78 tff(uri_ex_hasFather_type, type, (
% 0.80/0.78 uri_ex_hasFather: $i)).
% 0.80/0.78 tff(ip_type, type, (
% 0.80/0.78 ip: $i > $o)).
% 0.80/0.78 tff(tptp_fun_BNODE_l11_144_type, type, (
% 0.80/0.78 tptp_fun_BNODE_l11_144: $i)).
% 0.80/0.78 tff(uri_owl_propertyChainAxiom_type, type, (
% 0.80/0.78 uri_owl_propertyChainAxiom: $i)).
% 0.80/0.78 tff(tptp_fun_Y2_100_type, type, (
% 0.80/0.78 tptp_fun_Y2_100: ( $i * $i * $i ) > $i)).
% 0.80/0.78 tff(tptp_fun_Y1_101_type, type, (
% 0.80/0.78 tptp_fun_Y1_101: ( $i * $i * $i ) > $i)).
% 0.80/0.78 tff(tptp_fun_Y0_102_type, type, (
% 0.80/0.78 tptp_fun_Y0_102: ( $i * $i * $i ) > $i)).
% 0.80/0.78 tff(uri_rdf_nil_type, type, (
% 0.80/0.78 uri_rdf_nil: $i)).
% 0.80/0.78 tff(tptp_fun_BNODE_l12_143_type, type, (
% 0.80/0.78 tptp_fun_BNODE_l12_143: $i)).
% 0.80/0.78 tff(uri_rdf_rest_type, type, (
% 0.80/0.78 uri_rdf_rest: $i)).
% 0.80/0.78 tff(uri_ex_dave_type, type, (
% 0.80/0.78 uri_ex_dave: $i)).
% 0.80/0.78 tff(uri_ex_bob_type, type, (
% 0.80/0.78 uri_ex_bob: $i)).
% 0.80/0.78 tff(uri_ex_charly_type, type, (
% 0.80/0.78 uri_ex_charly: $i)).
% 0.80/0.78 tff(uri_ex_alice_type, type, (
% 0.80/0.78 uri_ex_alice: $i)).
% 0.80/0.78 tff(tptp_fun_BNODE_l3_140_type, type, (
% 0.80/0.78 tptp_fun_BNODE_l3_140: $i)).
% 0.80/0.78 tff(uri_owl_inverseOf_type, type, (
% 0.80/0.78 uri_owl_inverseOf: $i)).
% 0.80/0.78 tff(tptp_fun_BNODE_l22_141_type, type, (
% 0.80/0.78 tptp_fun_BNODE_l22_141: $i)).
% 0.80/0.78 tff(uri_rdf_first_type, type, (
% 0.80/0.78 uri_rdf_first: $i)).
% 0.80/0.78 tff(tptp_fun_BNODE_l21_142_type, type, (
% 0.80/0.78 tptp_fun_BNODE_l21_142: $i)).
% 0.80/0.78 tff(tptp_fun_X_108_type, type, (
% 0.80/0.78 tptp_fun_X_108: ( $i * $i ) > $i)).
% 0.80/0.78 tff(tptp_fun_Y_107_type, type, (
% 0.80/0.78 tptp_fun_Y_107: ( $i * $i ) > $i)).
% 0.80/0.78 tff(1,plain,
% 0.80/0.78 (?[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))),
% 0.80/0.78 inference(rewrite,[status(thm)],[])).
% 0.80/0.78 tff(2,plain,
% 0.80/0.78 (^[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))))),
% 0.80/0.80 inference(bind,[status(th)],[])).
% 0.80/0.80 tff(3,plain,
% 0.80/0.80 (?[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))),
% 0.80/0.80 inference(quant_intro,[status(thm)],[2])).
% 0.80/0.80 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')).
% 0.80/0.80 tff(5,plain,
% 0.80/0.80 (?[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))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.80/0.80 tff(6,plain,
% 0.80/0.80 (?[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))),
% 0.80/0.80 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.80/0.80 tff(7,plain,(
% 0.80/0.80 iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) & iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin) & iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143) & iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather) & iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) & iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle) & iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141) & iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140) & iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil) & iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)),
% 0.80/0.80 inference(skolemize,[status(sab)],[6])).
% 0.80/0.80 tff(8,plain,
% 0.80/0.80 (iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)),
% 0.80/0.80 inference(and_elim,[status(thm)],[7])).
% 0.80/0.80 tff(9,plain,
% 0.80/0.80 (iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)),
% 0.80/0.80 inference(and_elim,[status(thm)],[7])).
% 0.80/0.80 tff(10,plain,
% 0.80/0.80 (iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)),
% 0.80/0.80 inference(and_elim,[status(thm)],[7])).
% 0.80/0.80 tff(11,plain,
% 0.80/0.80 (iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)),
% 0.80/0.80 inference(and_elim,[status(thm)],[7])).
% 0.80/0.80 tff(12,plain,
% 0.80/0.80 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))))))), (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))))))))), rewrite(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))), (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))))),
% 0.80/0.80 inference(bind,[status(th)],[])).
% 0.80/0.80 tff(13,plain,
% 0.80/0.80 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))),
% 0.80/0.80 inference(quant_intro,[status(thm)],[12])).
% 0.80/0.80 tff(14,plain,
% 0.80/0.80 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : refl(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))))),
% 0.80/0.80 inference(bind,[status(th)],[])).
% 0.80/0.80 tff(15,plain,
% 0.80/0.80 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.80/0.80 inference(quant_intro,[status(thm)],[14])).
% 0.80/0.80 tff(16,plain,
% 0.80/0.80 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : rewrite(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))))),
% 0.80/0.80 inference(bind,[status(th)],[])).
% 0.80/0.80 tff(17,plain,
% 0.80/0.80 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.80/0.80 inference(quant_intro,[status(thm)],[16])).
% 0.80/0.80 tff(18,plain,
% 0.80/0.80 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.80/0.80 inference(transitivity,[status(thm)],[17, 15])).
% 0.80/0.80 tff(19,plain,
% 0.80/0.80 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) <=> ((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))), trans(monotonicity(rewrite((~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) <=> (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))) <=> (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))), rewrite((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) <=> (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))))), rewrite((((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))))),
% 0.80/0.80 inference(bind,[status(th)],[])).
% 0.80/0.80 tff(20,plain,
% 0.80/0.80 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.80/0.81 inference(quant_intro,[status(thm)],[19])).
% 0.80/0.81 tff(21,plain,
% 0.80/0.81 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : rewrite(((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))),
% 0.80/0.81 inference(bind,[status(th)],[])).
% 0.80/0.81 tff(22,plain,
% 0.80/0.81 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))),
% 0.80/0.81 inference(quant_intro,[status(thm)],[21])).
% 0.80/0.81 tff(23,plain,
% 0.80/0.81 (![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)))))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(24,plain,
% 0.80/0.81 (^[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)))))))),
% 0.80/0.81 inference(bind,[status(th)],[])).
% 0.80/0.81 tff(25,plain,
% 0.80/0.81 (![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)))))),
% 0.80/0.81 inference(quant_intro,[status(thm)],[24])).
% 0.80/0.81 tff(26,axiom,(![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_chain_002')).
% 0.80/0.81 tff(27,plain,
% 0.80/0.81 (![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)))))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.80/0.81 tff(28,plain,
% 0.80/0.81 (![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)))))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.80/0.81 tff(29,plain,(
% 0.80/0.81 ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))),
% 0.80/0.81 inference(skolemize,[status(sab)],[28])).
% 0.80/0.81 tff(30,plain,
% 0.80/0.81 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.80/0.81 tff(31,plain,
% 0.80/0.81 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.80/0.81 tff(32,plain,
% 0.80/0.81 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[31, 18])).
% 0.80/0.81 tff(33,plain,
% 0.80/0.81 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))),
% 0.80/0.81 inference(modus_ponens,[status(thm)],[32, 13])).
% 0.80/0.81 tff(34,plain,
% 0.80/0.81 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(35,plain,
% 0.80/0.81 (((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(36,plain,
% 0.80/0.81 ((~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))))))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(37,plain,
% 0.80/0.81 (((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))))),
% 0.80/0.81 inference(monotonicity,[status(thm)],[36])).
% 0.80/0.81 tff(38,plain,
% 0.80/0.81 (((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))))),
% 0.80/0.81 inference(transitivity,[status(thm)],[37, 35])).
% 0.80/0.81 tff(39,plain,
% 0.80/0.81 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))))))))),
% 0.80/0.82 inference(monotonicity,[status(thm)],[38])).
% 0.80/0.82 tff(40,plain,
% 0.80/0.82 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))))),
% 0.80/0.82 inference(transitivity,[status(thm)],[39, 34])).
% 0.80/0.82 tff(41,plain,
% 0.80/0.82 ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~ip(uri_ex_hasUncle)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasUncle, Y0, Y2) | (~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)))))))))))),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(42,plain,
% 0.80/0.82 ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l11!144, uri_ex_hasCousin)) | (~iext(uri_rdf_rest, BNODE_l11!144, BNODE_l12!143)) | (~iext(uri_rdf_first, BNODE_l12!143, uri_ex_hasFather)) | (~iext(uri_rdf_rest, BNODE_l12!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))))))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.80/0.82 tff(43,plain,
% 0.80/0.82 (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[42, 33, 11, 10, 9, 8])).
% 0.80/0.82 tff(44,plain,
% 0.80/0.82 (((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasUncle, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle)) | (~iext(uri_ex_hasCousin, tptp_fun_Y0_102(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))) | (~iext(uri_ex_hasFather, tptp_fun_Y1_101(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle), tptp_fun_Y2_100(uri_ex_hasFather, uri_ex_hasCousin, uri_ex_hasUncle))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))))) | ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))),
% 0.80/0.82 inference(tautology,[status(thm)],[])).
% 0.80/0.82 tff(45,plain,
% 0.80/0.82 ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.80/0.82 tff(46,plain,
% 0.80/0.82 (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)),
% 0.80/0.82 inference(and_elim,[status(thm)],[7])).
% 0.80/0.82 tff(47,plain,
% 0.80/0.82 ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))) | (~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))),
% 0.80/0.82 inference(tautology,[status(thm)],[])).
% 0.80/0.82 tff(48,plain,
% 0.80/0.82 ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l11!144)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))))) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.80/0.82 tff(49,plain,
% 0.80/0.82 (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.80/0.82 tff(50,plain,
% 0.80/0.82 (((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasFather)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2)))) | ![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))),
% 0.80/0.82 inference(tautology,[status(thm)],[])).
% 0.80/0.82 tff(51,plain,
% 0.80/0.82 (![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.80/0.82 tff(52,plain,
% 0.80/0.82 (iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)),
% 0.80/0.82 inference(and_elim,[status(thm)],[7])).
% 0.80/0.82 tff(53,plain,
% 0.80/0.82 (iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)),
% 0.80/0.82 inference(and_elim,[status(thm)],[7])).
% 0.80/0.82 tff(54,plain,
% 0.80/0.82 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))))))),
% 0.80/0.82 inference(bind,[status(th)],[])).
% 0.80/0.82 tff(55,plain,
% 0.80/0.82 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> ![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.80/0.82 inference(quant_intro,[status(thm)],[54])).
% 0.80/0.82 tff(56,plain,
% 0.80/0.82 (^[P1: $i, P2: $i] : refl((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.80/0.82 inference(bind,[status(th)],[])).
% 0.80/0.82 tff(57,plain,
% 0.80/0.82 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))),
% 0.80/0.82 inference(quant_intro,[status(thm)],[56])).
% 0.80/0.82 tff(58,plain,
% 0.80/0.82 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))))),
% 0.80/0.82 inference(bind,[status(th)],[])).
% 0.80/0.82 tff(59,plain,
% 0.80/0.82 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))),
% 0.80/0.82 inference(quant_intro,[status(thm)],[58])).
% 0.80/0.82 tff(60,plain,
% 0.80/0.82 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))),
% 0.80/0.82 inference(transitivity,[status(thm)],[59, 57])).
% 0.80/0.82 tff(61,plain,
% 0.80/0.82 (^[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_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))) <=> (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))), ((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) <=> (((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))), rewrite((((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))), ((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) <=> (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))))),
% 0.80/0.82 inference(bind,[status(th)],[])).
% 0.80/0.82 tff(62,plain,
% 0.80/0.82 (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))),
% 0.80/0.82 inference(quant_intro,[status(thm)],[61])).
% 0.80/0.82 tff(63,plain,
% 0.80/0.82 (^[P1: $i, P2: $i] : rewrite((((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))),
% 0.80/0.82 inference(bind,[status(th)],[])).
% 0.80/0.82 tff(64,plain,
% 0.80/0.82 (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))))) <=> ![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))),
% 0.80/0.82 inference(quant_intro,[status(thm)],[63])).
% 0.80/0.82 tff(65,plain,
% 0.80/0.82 (![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))))),
% 0.80/0.82 inference(rewrite,[status(thm)],[])).
% 0.80/0.82 tff(66,plain,
% 0.80/0.82 (^[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)))))),
% 0.80/0.82 inference(bind,[status(th)],[])).
% 0.80/0.82 tff(67,plain,
% 0.80/0.82 (![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))))),
% 0.80/0.82 inference(quant_intro,[status(thm)],[66])).
% 0.80/0.82 tff(68,axiom,(![P1: $i, P2: $i] : (iext(uri_owl_inverseOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_inv')).
% 0.80/0.82 tff(69,plain,
% 0.80/0.82 (![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))))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.80/0.82 tff(70,plain,
% 0.80/0.82 (![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))))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.80/0.82 tff(71,plain,(
% 0.80/0.82 ![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~(iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1)) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))),
% 0.80/0.82 inference(skolemize,[status(sab)],[70])).
% 0.80/0.82 tff(72,plain,
% 0.80/0.82 (![P1: $i, P2: $i] : (((~iext(uri_owl_inverseOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))) & (iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.80/0.82 tff(73,plain,
% 0.80/0.82 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.80/0.82 tff(74,plain,
% 0.80/0.82 (![P1: $i, P2: $i] : (~((~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X))))))) | (~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1)))))))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[73, 60])).
% 0.80/0.82 tff(75,plain,
% 0.80/0.82 (![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))),
% 0.80/0.82 inference(modus_ponens,[status(thm)],[74, 55])).
% 0.80/0.82 tff(76,plain,
% 0.80/0.82 ((~![P1: $i, P2: $i] : (~((~(iext(uri_owl_inverseOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | ((~iext(P1, tptp_fun_X_108(P2, P1), tptp_fun_Y_107(P2, P1))) <=> iext(P2, tptp_fun_Y_107(P2, P1), tptp_fun_X_108(P2, P1))))) | (~((~iext(uri_owl_inverseOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : (iext(P1, X, Y) <=> iext(P2, Y, X)))))))))) | (~((~(iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather) | (~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | ((~iext(BNODE_l3!140, tptp_fun_X_108(uri_ex_hasFather, BNODE_l3!140), tptp_fun_Y_107(uri_ex_hasFather, BNODE_l3!140))) <=> iext(uri_ex_hasFather, tptp_fun_Y_107(uri_ex_hasFather, BNODE_l3!140), tptp_fun_X_108(uri_ex_hasFather, BNODE_l3!140))))) | (~((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))))))),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(77,plain,
% 0.80/0.82 (~((~(iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather) | (~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | ((~iext(BNODE_l3!140, tptp_fun_X_108(uri_ex_hasFather, BNODE_l3!140), tptp_fun_Y_107(uri_ex_hasFather, BNODE_l3!140))) <=> iext(uri_ex_hasFather, tptp_fun_Y_107(uri_ex_hasFather, BNODE_l3!140), tptp_fun_X_108(uri_ex_hasFather, BNODE_l3!140))))) | (~((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))))))))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.80/0.82 tff(78,plain,
% 0.80/0.82 (((~(iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather) | (~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | ((~iext(BNODE_l3!140, tptp_fun_X_108(uri_ex_hasFather, BNODE_l3!140), tptp_fun_Y_107(uri_ex_hasFather, BNODE_l3!140))) <=> iext(uri_ex_hasFather, tptp_fun_Y_107(uri_ex_hasFather, BNODE_l3!140), tptp_fun_X_108(uri_ex_hasFather, BNODE_l3!140))))) | (~((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))))) | ((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))))))),
% 0.80/0.82 inference(tautology,[status(thm)],[])).
% 0.80/0.82 tff(79,plain,
% 0.80/0.82 ((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.80/0.82 tff(80,plain,
% 0.80/0.82 (iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)),
% 0.80/0.82 inference(and_elim,[status(thm)],[7])).
% 0.80/0.82 tff(81,plain,
% 0.80/0.82 ((~((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))))))) | (~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))),
% 0.80/0.82 inference(tautology,[status(thm)],[])).
% 0.80/0.82 tff(82,plain,
% 0.80/0.82 ((~((~iext(uri_owl_inverseOf, BNODE_l3!140, uri_ex_hasFather)) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))))))) | (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X)))))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.80/0.82 tff(83,plain,
% 0.80/0.82 (~((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.80/0.82 tff(84,plain,
% 0.80/0.82 (((~ip(uri_ex_hasFather)) | (~ip(BNODE_l3!140)) | (~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X)))) | ![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))),
% 0.80/0.82 inference(tautology,[status(thm)],[])).
% 0.80/0.82 tff(85,plain,
% 0.80/0.82 (![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.80/0.82 tff(86,plain,
% 0.80/0.82 ((~![X: $i, Y: $i] : (iext(BNODE_l3!140, X, Y) <=> iext(uri_ex_hasFather, Y, X))) | (iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))),
% 0.80/0.82 inference(quant_inst,[status(thm)],[])).
% 0.80/0.82 tff(87,plain,
% 0.80/0.82 (iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.80/0.82 tff(88,plain,
% 0.80/0.82 (iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)),
% 0.80/0.82 inference(and_elim,[status(thm)],[7])).
% 0.80/0.82 tff(89,plain,
% 0.80/0.82 ((~(iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))) | iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice) | (~iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))),
% 0.80/0.82 inference(tautology,[status(thm)],[])).
% 0.80/0.82 tff(90,plain,
% 0.80/0.82 ((~(iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))) | iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.80/0.82 tff(91,plain,
% 0.80/0.82 (iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice)),
% 0.80/0.82 inference(unit_resolution,[status(thm)],[90, 87])).
% 0.80/0.82 tff(92,plain,
% 0.80/0.82 (iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)),
% 0.80/0.82 inference(and_elim,[status(thm)],[7])).
% 0.80/0.82 tff(93,plain,
% 0.80/0.82 (iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)),
% 0.80/0.82 inference(and_elim,[status(thm)],[7])).
% 0.80/0.82 tff(94,plain,
% 0.80/0.82 (iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)),
% 0.80/0.82 inference(and_elim,[status(thm)],[7])).
% 0.80/0.82 tff(95,plain,
% 0.80/0.82 (iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)),
% 0.80/0.82 inference(and_elim,[status(thm)],[7])).
% 0.80/0.82 tff(96,plain,
% 0.80/0.82 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))))),
% 0.80/0.83 inference(rewrite,[status(thm)],[])).
% 0.80/0.83 tff(97,plain,
% 0.80/0.83 (((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))))),
% 0.80/0.83 inference(rewrite,[status(thm)],[])).
% 0.80/0.83 tff(98,plain,
% 0.80/0.83 ((~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))))))),
% 0.80/0.83 inference(rewrite,[status(thm)],[])).
% 0.80/0.83 tff(99,plain,
% 0.80/0.83 (((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))))),
% 0.80/0.83 inference(monotonicity,[status(thm)],[98])).
% 0.80/0.83 tff(100,plain,
% 0.80/0.83 (((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))))),
% 0.80/0.83 inference(transitivity,[status(thm)],[99, 97])).
% 0.80/0.83 tff(101,plain,
% 0.80/0.83 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))))))))),
% 0.80/0.83 inference(monotonicity,[status(thm)],[100])).
% 0.80/0.83 tff(102,plain,
% 0.80/0.83 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))))),
% 0.80/0.83 inference(transitivity,[status(thm)],[101, 96])).
% 0.80/0.83 tff(103,plain,
% 0.80/0.83 ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(BNODE_l3!140)) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_ex_hasCousin, Y0, Y2) | (~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)))))))))))),
% 0.80/0.83 inference(quant_inst,[status(thm)],[])).
% 0.80/0.83 tff(104,plain,
% 0.80/0.83 ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!142, uri_ex_hasUncle)) | (~iext(uri_rdf_first, BNODE_l22!141, BNODE_l3!140)) | (~iext(uri_rdf_rest, BNODE_l21!142, BNODE_l22!141)) | (~iext(uri_rdf_rest, BNODE_l22!141, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))))))),
% 0.80/0.83 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.80/0.83 tff(105,plain,
% 0.80/0.83 (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))))),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[104, 33, 95, 94, 93, 92])).
% 0.80/0.83 tff(106,plain,
% 0.80/0.83 (((~(iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142) | (~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~(iext(uri_ex_hasCousin, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin)) | (~iext(uri_ex_hasUncle, tptp_fun_Y0_102(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))) | (~iext(BNODE_l3!140, tptp_fun_Y1_101(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin), tptp_fun_Y2_100(BNODE_l3!140, uri_ex_hasUncle, uri_ex_hasCousin))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))))) | ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))),
% 0.80/0.83 inference(tautology,[status(thm)],[])).
% 0.80/0.83 tff(107,plain,
% 0.80/0.83 ((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.80/0.83 tff(108,plain,
% 0.80/0.83 (iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)),
% 0.80/0.83 inference(and_elim,[status(thm)],[7])).
% 0.80/0.83 tff(109,plain,
% 0.80/0.83 ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))) | (~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))),
% 0.80/0.83 inference(tautology,[status(thm)],[])).
% 0.80/0.83 tff(110,plain,
% 0.80/0.83 ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l21!142)) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))))) | (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))))),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.80/0.83 tff(111,plain,
% 0.80/0.83 (~((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))))),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[110, 107])).
% 0.80/0.83 tff(112,plain,
% 0.80/0.83 (((~ip(uri_ex_hasUncle)) | (~ip(uri_ex_hasCousin)) | (~ip(BNODE_l3!140)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2)))) | ![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))),
% 0.80/0.83 inference(tautology,[status(thm)],[])).
% 0.80/0.83 tff(113,plain,
% 0.80/0.83 (![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.80/0.83 tff(114,plain,
% 0.80/0.83 (iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)),
% 0.80/0.83 inference(and_elim,[status(thm)],[7])).
% 0.80/0.83 tff(115,assumption,(~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)), introduced(assumption)).
% 0.80/0.83 tff(116,plain,
% 0.80/0.83 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))) | ((~iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) | iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))) | (~iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) | iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))),
% 0.80/0.83 inference(rewrite,[status(thm)],[])).
% 0.80/0.83 tff(117,plain,
% 0.80/0.83 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))) | ((~iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) | iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))),
% 0.80/0.83 inference(quant_inst,[status(thm)],[])).
% 0.80/0.83 tff(118,plain,
% 0.80/0.83 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_l3!140, Y1, Y2)) | (~iext(uri_ex_hasUncle, Y0, Y1)) | iext(uri_ex_hasCousin, Y0, Y2))) | (~iext(BNODE_l3!140, uri_ex_dave, uri_ex_alice)) | (~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) | iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)),
% 0.80/0.83 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.80/0.83 tff(119,plain,
% 0.80/0.83 ($false),
% 0.80/0.83 inference(unit_resolution,[status(thm)],[118, 115, 114, 113, 91])).
% 0.80/0.83 tff(120,plain,(iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)), inference(lemma,lemma(discharge,[]))).
% 0.80/0.83 tff(121,plain,
% 0.80/0.83 ((~(~((~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)))),
% 0.80/0.83 inference(rewrite,[status(thm)],[])).
% 0.80/0.83 tff(122,plain,
% 0.80/0.83 ((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))))),
% 0.80/0.83 inference(rewrite,[status(thm)],[])).
% 0.80/0.83 tff(123,plain,
% 0.80/0.83 ((~(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)))))),
% 0.80/0.83 inference(monotonicity,[status(thm)],[122])).
% 0.80/0.83 tff(124,plain,
% 0.80/0.83 ((~(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)))),
% 0.80/0.83 inference(transitivity,[status(thm)],[123, 121])).
% 0.80/0.83 tff(125,plain,
% 0.80/0.83 ((~(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)))),
% 0.80/0.83 inference(rewrite,[status(thm)],[])).
% 0.80/0.83 tff(126,axiom,(~(iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_025_Cyclic_Dependencies_between_Complex_Properties')).
% 0.88/0.85 tff(127,plain,
% 0.88/0.85 (~(iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.88/0.85 tff(128,plain,
% 0.88/0.85 ((~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[127, 124])).
% 0.88/0.85 tff(129,plain,
% 0.88/0.85 (~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[128, 120])).
% 0.88/0.85 tff(130,plain,
% 0.88/0.85 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | (iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(131,plain,
% 0.88/0.85 (((~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)) <=> (iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)))),
% 0.88/0.85 inference(rewrite,[status(thm)],[])).
% 0.88/0.85 tff(132,plain,
% 0.88/0.85 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | ((~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | (iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly))))),
% 0.88/0.85 inference(monotonicity,[status(thm)],[131])).
% 0.88/0.85 tff(133,plain,
% 0.88/0.85 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | ((~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)))),
% 0.88/0.85 inference(transitivity,[status(thm)],[132, 130])).
% 0.88/0.85 tff(134,plain,
% 0.88/0.85 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | ((~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly))),
% 0.88/0.85 inference(quant_inst,[status(thm)],[])).
% 0.88/0.85 tff(135,plain,
% 0.88/0.85 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_ex_hasFather, Y1, Y2)) | (~iext(uri_ex_hasCousin, Y0, Y1)) | iext(uri_ex_hasUncle, Y0, Y2))) | iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) | (~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)) | (~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly))),
% 0.88/0.85 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.88/0.85 tff(136,plain,
% 0.88/0.85 ($false),
% 0.88/0.85 inference(unit_resolution,[status(thm)],[135, 129, 53, 52, 51])).
% 0.88/0.85 % SZS output end Proof
%------------------------------------------------------------------------------