TSTP Solution File: SWB025+2 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SWB025+2 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n002.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 08:22:10 EDT 2022
% Result : Theorem 18.18s 4.51s
% Output : Proof 18.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWB025+2 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.14 % Command : goeland -dmt -presko -proof %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 19:59:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 [DMT] DMT loaded with preskolemization
% 0.14/0.35 [EQ] equality loaded.
% 0.14/0.35 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.14/0.36 Start search
% 0.14/0.36 nb_step : 1 - limit : 5
% 0.14/0.36 Launch Gotab with destructive = true
% 18.18/4.48 % SZS output start Proof for theBenchmark.p
% 18.18/4.50 [0] ALPHA_AND : (! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22))))))) & ? [BNODE_l1127_27, BNODE_l1228_28, BNODE_l2129_29, BNODE_l2230_30, BNODE_l331_31] : (((((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l1127_27) & iext(uri_rdf_first, BNODE_l1127_27, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l1127_27, BNODE_l1228_28)) & iext(uri_rdf_first, BNODE_l1228_28, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l1228_28, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l2129_29)) & iext(uri_rdf_first, BNODE_l2129_29, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l2129_29, BNODE_l2230_30)) & iext(uri_rdf_first, BNODE_l2230_30, BNODE_l331_31)) & iext(uri_rdf_rest, BNODE_l2230_30, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l331_31, 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_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)))
% 18.18/4.50 -> [1] ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22))))))), ? [BNODE_l1127_27, BNODE_l1228_28, BNODE_l2129_29, BNODE_l2230_30, BNODE_l331_31] : (((((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l1127_27) & iext(uri_rdf_first, BNODE_l1127_27, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l1127_27, BNODE_l1228_28)) & iext(uri_rdf_first, BNODE_l1228_28, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l1228_28, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l2129_29)) & iext(uri_rdf_first, BNODE_l2129_29, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l2129_29, BNODE_l2230_30)) & iext(uri_rdf_first, BNODE_l2230_30, BNODE_l331_31)) & iext(uri_rdf_rest, BNODE_l2230_30, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l331_31, 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_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))
% 18.18/4.50
% 18.18/4.50 [1] DELTA_EXISTS : ? [BNODE_l1127_27, BNODE_l1228_28, BNODE_l2129_29, BNODE_l2230_30, BNODE_l331_31] : (((((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, BNODE_l1127_27) & iext(uri_rdf_first, BNODE_l1127_27, uri_ex_hasCousin)) & iext(uri_rdf_rest, BNODE_l1127_27, BNODE_l1228_28)) & iext(uri_rdf_first, BNODE_l1228_28, uri_ex_hasFather)) & iext(uri_rdf_rest, BNODE_l1228_28, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, BNODE_l2129_29)) & iext(uri_rdf_first, BNODE_l2129_29, uri_ex_hasUncle)) & iext(uri_rdf_rest, BNODE_l2129_29, BNODE_l2230_30)) & iext(uri_rdf_first, BNODE_l2230_30, BNODE_l331_31)) & iext(uri_rdf_rest, BNODE_l2230_30, uri_rdf_nil)) & iext(uri_owl_inverseOf, BNODE_l331_31, 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)))
% 18.18/4.50 -> [2] ((((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) & iext(uri_owl_inverseOf, skolem_BNODE_l33131, 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))
% 18.18/4.50
% 18.18/4.50 [2] ALPHA_AND : ((((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) & iext(uri_owl_inverseOf, skolem_BNODE_l33131, 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))
% 18.18/4.50 -> [3] (((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) & iext(uri_owl_inverseOf, skolem_BNODE_l33131, 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)
% 18.18/4.50
% 18.18/4.50 [3] ALPHA_AND : (((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) & iext(uri_owl_inverseOf, skolem_BNODE_l33131, 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))
% 18.18/4.50 -> [4] ((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) & iext(uri_owl_inverseOf, skolem_BNODE_l33131, 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)
% 18.18/4.50
% 18.18/4.50 [4] ALPHA_AND : ((((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) & iext(uri_owl_inverseOf, skolem_BNODE_l33131, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)) & iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob))
% 18.18/4.50 -> [5] (((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) & iext(uri_owl_inverseOf, skolem_BNODE_l33131, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)), iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)
% 18.18/4.50
% 18.18/4.50 [5] ALPHA_AND : (((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) & iext(uri_owl_inverseOf, skolem_BNODE_l33131, uri_ex_hasFather)) & iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))
% 18.18/4.50 -> [6] ((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) & iext(uri_owl_inverseOf, skolem_BNODE_l33131, uri_ex_hasFather)), iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)
% 18.18/4.50
% 18.18/4.50 [6] ALPHA_AND : ((((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) & iext(uri_owl_inverseOf, skolem_BNODE_l33131, uri_ex_hasFather))
% 18.18/4.50 -> [7] (((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)), iext(uri_owl_inverseOf, skolem_BNODE_l33131, uri_ex_hasFather)
% 18.18/4.50
% 18.18/4.50 [7] Rewrite : iext(uri_owl_inverseOf, skolem_BNODE_l33131, uri_ex_hasFather)
% 18.18/4.50 -> [8] ((ip(skolem_BNODE_l33131) & ip(uri_ex_hasFather)) & ! [X25_25, Y26_26] : ((iext(skolem_BNODE_l33131, X25_25, Y26_26) <=> iext(uri_ex_hasFather, Y26_26, X25_25))))
% 18.18/4.50
% 18.18/4.50 [8] ALPHA_AND : (((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil))
% 18.18/4.50 -> [9] ((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)), iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)
% 18.18/4.50
% 18.18/4.50 [9] ALPHA_AND : ((ip(skolem_BNODE_l33131) & ip(uri_ex_hasFather)) & ! [X25_25, Y26_26] : ((iext(skolem_BNODE_l33131, X25_25, Y26_26) <=> iext(uri_ex_hasFather, Y26_26, X25_25))))
% 18.18/4.50 -> [10] (ip(skolem_BNODE_l33131) & ip(uri_ex_hasFather)), ! [X25_25, Y26_26] : ((iext(skolem_BNODE_l33131, X25_25, Y26_26) <=> iext(uri_ex_hasFather, Y26_26, X25_25)))
% 18.18/4.50
% 18.18/4.50 [10] ALPHA_AND : ((((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131))
% 18.18/4.50 -> [11] (((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)), iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)
% 18.18/4.50
% 18.18/4.50 [11] ALPHA_AND : (ip(skolem_BNODE_l33131) & ip(uri_ex_hasFather))
% 18.18/4.50 -> [12] ip(skolem_BNODE_l33131), ip(uri_ex_hasFather)
% 18.18/4.50
% 18.18/4.50 [12] ALPHA_AND : (((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030))
% 18.18/4.50 -> [13] ((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)), iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)
% 18.18/4.50
% 18.18/4.50 [13] ALPHA_AND : ((((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)) & iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle))
% 18.18/4.50 -> [14] (((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)), iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)
% 18.18/4.50
% 18.18/4.50 [14] ALPHA_AND : (((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929))
% 18.18/4.50 -> [15] ((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)), iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)
% 18.18/4.50
% 18.18/4.50 [15] ALPHA_AND : ((((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil))
% 18.18/4.50 -> [16] (((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)), iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)
% 18.18/4.50
% 18.18/4.50 [16] ALPHA_AND : (((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather))
% 18.18/4.50 -> [17] ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)), iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)
% 18.18/4.50
% 18.18/4.50 [17] ALPHA_AND : ((iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828))
% 18.18/4.50 -> [18] (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)), iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)
% 18.18/4.50
% 18.18/4.50 [18] ALPHA_AND : (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) & iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin))
% 18.18/4.50 -> [19] iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727), iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)
% 18.18/4.50
% 18.18/4.50 [19] BETA_NOT_AND : ~(iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly) & iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))
% 18.18/4.50 -> [20] ~iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)
% 18.18/4.50 -> [21] ~iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)
% 18.18/4.50
% 18.18/4.50 [21] GAMMA_FORALL : ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.50 -> [25] ((((iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929) <=> (((ip(uri_ex_hasCousin) & ip(uri_ex_hasUncle)) & ip(skolem_BNODE_l33131)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasUncle, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22))))))
% 18.18/4.50
% 18.18/4.50 [25] BETA_IMPLY : ((((iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929) <=> (((ip(uri_ex_hasCousin) & ip(uri_ex_hasUncle)) & ip(skolem_BNODE_l33131)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasUncle, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22))))))
% 18.18/4.50 -> [28] ~(((iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil))
% 18.18/4.50 -> [29] (iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929) <=> (((ip(uri_ex_hasCousin) & ip(uri_ex_hasUncle)) & ip(skolem_BNODE_l33131)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasUncle, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22)))))
% 18.18/4.50
% 18.18/4.50 [28] BETA_NOT_AND : ~(((iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil))
% 18.18/4.50 -> [34] ~((iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131))
% 18.18/4.50 -> [35] ~iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)
% 18.18/4.50
% 18.18/4.50 [35] CLOSURE : ~iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)
% 18.18/4.50
% 18.18/4.50 [34] BETA_NOT_AND : ~((iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131))
% 18.18/4.50 -> [68] ~(iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030))
% 18.18/4.50 -> [69] ~iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)
% 18.18/4.50
% 18.18/4.50 [69] CLOSURE : ~iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)
% 18.18/4.50
% 18.18/4.50 [68] BETA_NOT_AND : ~(iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030))
% 18.18/4.50 -> [79] ~iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)
% 18.18/4.50 -> [80] ~iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)
% 18.18/4.50
% 18.18/4.50 [80] CLOSURE : ~iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)
% 18.18/4.50
% 18.18/4.50 [79] CLOSURE : ~iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasUncle)
% 18.18/4.50
% 18.18/4.50 [29] BETA_EQUIV : (iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929) <=> (((ip(uri_ex_hasCousin) & ip(uri_ex_hasUncle)) & ip(skolem_BNODE_l33131)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasUncle, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22)))))
% 18.18/4.50 -> [311] ~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929), ~(((ip(uri_ex_hasCousin) & ip(uri_ex_hasUncle)) & ip(skolem_BNODE_l33131)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasUncle, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22))))
% 18.18/4.50 -> [312] iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929), (((ip(uri_ex_hasCousin) & ip(uri_ex_hasUncle)) & ip(skolem_BNODE_l33131)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasUncle, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22))))
% 18.18/4.50
% 18.18/4.50 [311] CLOSURE : ~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)
% 18.18/4.50
% 18.18/4.50 [312] ALPHA_AND : (((ip(uri_ex_hasCousin) & ip(uri_ex_hasUncle)) & ip(skolem_BNODE_l33131)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasUncle, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22))))
% 18.18/4.50 -> [313] ((ip(uri_ex_hasCousin) & ip(uri_ex_hasUncle)) & ip(skolem_BNODE_l33131)), ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasUncle, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22)))
% 18.18/4.50
% 18.18/4.50 [313] ALPHA_AND : ((ip(uri_ex_hasCousin) & ip(uri_ex_hasUncle)) & ip(skolem_BNODE_l33131))
% 18.18/4.50 -> [314] (ip(uri_ex_hasCousin) & ip(uri_ex_hasUncle)), ip(skolem_BNODE_l33131)
% 18.18/4.50
% 18.18/4.50 [314] ALPHA_AND : (ip(uri_ex_hasCousin) & ip(uri_ex_hasUncle))
% 18.18/4.50 -> [315] ip(uri_ex_hasCousin), ip(uri_ex_hasUncle)
% 18.18/4.50
% 18.18/4.50 [315] GAMMA_FORALL : ! [X25_25, Y26_26] : ((iext(skolem_BNODE_l33131, X25_25, Y26_26) <=> iext(uri_ex_hasFather, Y26_26, X25_25)))
% 18.18/4.50 -> [322] (iext(skolem_BNODE_l33131, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))
% 18.18/4.50
% 18.18/4.50 [322] BETA_EQUIV : (iext(skolem_BNODE_l33131, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))
% 18.18/4.50 -> [323] ~iext(skolem_BNODE_l33131, uri_ex_dave, uri_ex_alice), ~iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)
% 18.18/4.50 -> [324] iext(skolem_BNODE_l33131, uri_ex_dave, uri_ex_alice), iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)
% 18.18/4.50
% 18.18/4.50 [323] CLOSURE : ~iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)
% 18.18/4.50
% 18.18/4.50 [334] BETA_IMPLY : ((iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave) & iext(skolem_BNODE_l33131, uri_ex_dave, uri_ex_alice)) => iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice))
% 18.18/4.50 -> [369] ~(iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave) & iext(skolem_BNODE_l33131, uri_ex_dave, uri_ex_alice))
% 18.18/4.50 -> [370] iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)
% 18.18/4.50
% 18.18/4.50 [369] BETA_NOT_AND : ~(iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave) & iext(skolem_BNODE_l33131, uri_ex_dave, uri_ex_alice))
% 18.18/4.50 -> [375] ~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)
% 18.18/4.50 -> [376] ~iext(skolem_BNODE_l33131, uri_ex_dave, uri_ex_alice)
% 18.18/4.50
% 18.18/4.50 [376] CLOSURE : ~iext(skolem_BNODE_l33131, uri_ex_dave, uri_ex_alice)
% 18.18/4.50
% 18.18/4.50 [375] CLOSURE : ~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)
% 18.18/4.50
% 18.18/4.50 [370] CLOSURE : iext(uri_ex_hasCousin, uri_ex_bob, uri_ex_alice)
% 18.18/4.50
% 18.18/4.50 [20] GAMMA_FORALL : ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.50 -> [22] ((((iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929) <=> (((ip(uri_ex_hasCousin) & ip(uri_ex_hasCousin)) & ip(skolem_BNODE_l33131)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22))))))
% 18.18/4.50
% 18.18/4.50 [22] BETA_IMPLY : ((((iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929) <=> (((ip(uri_ex_hasCousin) & ip(uri_ex_hasCousin)) & ip(skolem_BNODE_l33131)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22))))))
% 18.18/4.50 -> [23] ~(((iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil))
% 18.18/4.50 -> [24] (iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929) <=> (((ip(uri_ex_hasCousin) & ip(uri_ex_hasCousin)) & ip(skolem_BNODE_l33131)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22)))))
% 18.18/4.50
% 18.18/4.50 [24] BETA_EQUIV : (iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929) <=> (((ip(uri_ex_hasCousin) & ip(uri_ex_hasCousin)) & ip(skolem_BNODE_l33131)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22)))))
% 18.18/4.50 -> [30] ~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929), ~(((ip(uri_ex_hasCousin) & ip(uri_ex_hasCousin)) & ip(skolem_BNODE_l33131)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22))))
% 18.18/4.50 -> [31] iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929), (((ip(uri_ex_hasCousin) & ip(uri_ex_hasCousin)) & ip(skolem_BNODE_l33131)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22))))
% 18.18/4.50
% 18.18/4.50 [30] CLOSURE : ~iext(uri_owl_propertyChainAxiom, uri_ex_hasCousin, skolem_BNODE_l212929)
% 18.18/4.50
% 18.18/4.50 [50] BETA_EQUIV : (iext(skolem_BNODE_l33131, uri_ex_bob, Y26_0_1) <=> iext(uri_ex_hasFather, Y26_0_1, uri_ex_bob))
% 18.18/4.50 -> [1207] ~iext(skolem_BNODE_l33131, uri_ex_bob, Y26_0_1), ~iext(uri_ex_hasFather, Y26_0_1, uri_ex_bob)
% 18.18/4.50 -> [1208] iext(skolem_BNODE_l33131, uri_ex_bob, Y26_0_1), iext(uri_ex_hasFather, Y26_0_1, uri_ex_bob)
% 18.18/4.50
% 18.18/4.50 [1208] GAMMA_FORALL : ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasUncle, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22)))
% 18.18/4.50 -> [1209] ((iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) => iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_dave))
% 18.18/4.50
% 18.18/4.50 [1209] BETA_IMPLY : ((iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)) => iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_dave))
% 18.18/4.50 -> [1210] ~(iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave))
% 18.18/4.50 -> [1211] iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_dave)
% 18.18/4.50
% 18.18/4.50 [1210] BETA_NOT_AND : ~(iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave))
% 18.18/4.50 -> [1212] ~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)
% 18.18/4.50 -> [1213] ~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)
% 18.18/4.50
% 18.18/4.50 [1212] CLOSURE : ~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)
% 18.18/4.50
% 18.18/4.50 [1213] CLOSURE : ~iext(uri_ex_hasUncle, uri_ex_bob, uri_ex_dave)
% 18.18/4.50
% 18.18/4.50 [1211] : ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.50 -> [1214] ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.50
% 18.18/4.50 [1214] GAMMA_FORALL : ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.50 -> [1217] ((((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))))
% 18.18/4.50
% 18.18/4.50 [1217] BETA_IMPLY : ((((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))))
% 18.18/4.50 -> [1218] ~(((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil))
% 18.18/4.50 -> [1219] (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22)))))
% 18.18/4.50
% 18.18/4.50 [1218] BETA_NOT_AND : ~(((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil))
% 18.18/4.50 -> [1222] ~((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather))
% 18.18/4.50 -> [1223] ~iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)
% 18.18/4.50
% 18.18/4.50 [1223] CLOSURE : ~iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)
% 18.18/4.50
% 18.18/4.50 [1222] BETA_NOT_AND : ~((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather))
% 18.18/4.50 -> [1254] ~(iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828))
% 18.18/4.50 -> [1255] ~iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)
% 18.18/4.50
% 18.18/4.50 [1255] CLOSURE : ~iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)
% 18.18/4.50
% 18.18/4.50 [1254] BETA_NOT_AND : ~(iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828))
% 18.18/4.50 -> [1264] ~iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)
% 18.18/4.50 -> [1265] ~iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)
% 18.18/4.50
% 18.18/4.50 [1264] CLOSURE : ~iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)
% 18.18/4.50
% 18.18/4.50 [1265] CLOSURE : ~iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)
% 18.18/4.50
% 18.18/4.50 [1219] BETA_EQUIV : (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22)))))
% 18.18/4.50 -> [1270] ~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727), ~(((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))
% 18.18/4.51 -> [1271] iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727), (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))
% 18.18/4.51
% 18.18/4.51 [1270] CLOSURE : ~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727)
% 18.18/4.51
% 18.18/4.51 [1271] ALPHA_AND : (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))
% 18.18/4.51 -> [1272] ((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)), ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22)))
% 18.18/4.51
% 18.18/4.51 [1272] ALPHA_AND : ((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather))
% 18.18/4.51 -> [1273] (ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)), ip(uri_ex_hasFather)
% 18.18/4.51
% 18.18/4.51 [1273] ALPHA_AND : (ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin))
% 18.18/4.51 -> [1274] ip(uri_ex_hasUncle), ip(uri_ex_hasCousin)
% 18.18/4.51
% 18.18/4.51 [1274] GAMMA_FORALL : ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22)))
% 18.18/4.51 -> [1275] ((iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) => iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly))
% 18.18/4.51
% 18.18/4.51 [1275] BETA_IMPLY : ((iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) => iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly))
% 18.18/4.51 -> [1276] ~(iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly))
% 18.18/4.51 -> [1277] iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [1276] BETA_NOT_AND : ~(iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly))
% 18.18/4.51 -> [1278] ~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)
% 18.18/4.51 -> [1279] ~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [1279] CLOSURE : ~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [1278] CLOSURE : ~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)
% 18.18/4.51
% 18.18/4.51 [1277] CLOSURE : iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [1207] GAMMA_FORALL : ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(skolem_BNODE_l33131, Y121_21, Y222_22)) => iext(uri_ex_hasCousin, Y020_20, Y222_22)))
% 18.18/4.51 -> [1280] ((iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(skolem_BNODE_l33131, uri_ex_bob, Y222_13_2)) => iext(uri_ex_hasCousin, uri_ex_alice, Y222_13_2))
% 18.18/4.51
% 18.18/4.51 [1280] BETA_IMPLY : ((iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(skolem_BNODE_l33131, uri_ex_bob, Y222_13_2)) => iext(uri_ex_hasCousin, uri_ex_alice, Y222_13_2))
% 18.18/4.51 -> [1281] ~(iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(skolem_BNODE_l33131, uri_ex_bob, Y222_13_2))
% 18.18/4.51 -> [1282] iext(uri_ex_hasCousin, uri_ex_alice, Y222_13_2)
% 18.18/4.51
% 18.18/4.51 [1282] : ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.51 -> [1285] ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.51
% 18.18/4.51 [1285] GAMMA_FORALL : ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.51 -> [1287] ((((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))))
% 18.18/4.51
% 18.18/4.51 [1287] BETA_IMPLY : ((((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))))
% 18.18/4.51 -> [1289] ~(((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil))
% 18.18/4.51 -> [1290] (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22)))))
% 18.18/4.51
% 18.18/4.51 [1289] BETA_NOT_AND : ~(((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil))
% 18.18/4.51 -> [1293] ~((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather))
% 18.18/4.51 -> [1294] ~iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)
% 18.18/4.51
% 18.18/4.51 [1293] BETA_NOT_AND : ~((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather))
% 18.18/4.51 -> [1299] ~(iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828))
% 18.18/4.51 -> [1300] ~iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)
% 18.18/4.51
% 18.18/4.51 [1300] CLOSURE : ~iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)
% 18.18/4.51
% 18.18/4.51 [1299] BETA_NOT_AND : ~(iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828))
% 18.18/4.51 -> [1325] ~iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)
% 18.18/4.51 -> [1326] ~iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)
% 18.18/4.51
% 18.18/4.51 [1325] CLOSURE : ~iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)
% 18.18/4.51
% 18.18/4.51 [1326] CLOSURE : ~iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)
% 18.18/4.51
% 18.18/4.51 [1294] CLOSURE : ~iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)
% 18.18/4.51
% 18.18/4.51 [1290] BETA_EQUIV : (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22)))))
% 18.18/4.51 -> [1359] ~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727), ~(((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))
% 18.18/4.51 -> [1360] iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727), (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))
% 18.18/4.51
% 18.18/4.51 [1359] CLOSURE : ~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727)
% 18.18/4.51
% 18.18/4.51 [1377] BETA_IMPLY : ((iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) => iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly))
% 18.18/4.51 -> [1424] ~(iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly))
% 18.18/4.51 -> [1425] iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [1425] CLOSURE : iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [1424] BETA_NOT_AND : ~(iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly))
% 18.18/4.51 -> [1430] ~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)
% 18.18/4.51 -> [1431] ~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [1430] CLOSURE : ~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)
% 18.18/4.51
% 18.18/4.51 [1431] CLOSURE : ~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [1281] BETA_NOT_AND : ~(iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(skolem_BNODE_l33131, uri_ex_bob, Y222_13_2))
% 18.18/4.51 -> [1283] ~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)
% 18.18/4.51 -> [1284] ~iext(skolem_BNODE_l33131, uri_ex_bob, Y222_13_2)
% 18.18/4.51
% 18.18/4.51 [1283] CLOSURE : ~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)
% 18.18/4.51
% 18.18/4.51 [1284] : ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.51 -> [1286] ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.51
% 18.18/4.51 [1286] GAMMA_FORALL : ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.51 -> [1288] ((((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))))
% 18.18/4.51
% 18.18/4.51 [1288] BETA_IMPLY : ((((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))))
% 18.18/4.51 -> [1291] ~(((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil))
% 18.18/4.51 -> [1292] (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22)))))
% 18.18/4.51
% 18.18/4.51 [1292] BETA_EQUIV : (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22)))))
% 18.18/4.51 -> [1301] ~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727), ~(((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))
% 18.18/4.51 -> [1302] iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727), (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))
% 18.18/4.51
% 18.18/4.51 [1301] CLOSURE : ~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727)
% 18.18/4.51
% 18.18/4.51 [1316] BETA_IMPLY : ((iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) => iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly))
% 18.18/4.51 -> [1422] ~(iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly))
% 18.18/4.51 -> [1423] iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [1423] CLOSURE : iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [1422] BETA_NOT_AND : ~(iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly))
% 18.18/4.51 -> [1432] ~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)
% 18.18/4.51 -> [1433] ~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [1432] CLOSURE : ~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)
% 18.18/4.51
% 18.18/4.51 [1433] CLOSURE : ~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [1291] BETA_NOT_AND : ~(((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil))
% 18.18/4.51 -> [1462] ~((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather))
% 18.18/4.51 -> [1463] ~iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)
% 18.18/4.51
% 18.18/4.51 [1463] CLOSURE : ~iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)
% 18.18/4.51
% 18.18/4.51 [1462] BETA_NOT_AND : ~((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather))
% 18.18/4.51 -> [1464] ~(iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828))
% 18.18/4.51 -> [1465] ~iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)
% 18.18/4.51
% 18.18/4.51 [1465] CLOSURE : ~iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)
% 18.18/4.51
% 18.18/4.51 [1464] BETA_NOT_AND : ~(iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828))
% 18.18/4.51 -> [1466] ~iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)
% 18.18/4.51 -> [1467] ~iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)
% 18.18/4.51
% 18.18/4.51 [1466] CLOSURE : ~iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)
% 18.18/4.51
% 18.18/4.51 [1467] CLOSURE : ~iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)
% 18.18/4.51
% 18.18/4.51 [23] BETA_NOT_AND : ~(((iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)) & iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil))
% 18.18/4.51 -> [1864] ~((iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131))
% 18.18/4.51 -> [1865] ~iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)
% 18.18/4.51
% 18.18/4.51 [1865] CLOSURE : ~iext(uri_rdf_rest, skolem_BNODE_l223030, uri_rdf_nil)
% 18.18/4.51
% 18.18/4.51 [1864] BETA_NOT_AND : ~((iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)) & iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131))
% 18.18/4.51 -> [1866] ~(iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030))
% 18.18/4.51 -> [1867] ~iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)
% 18.18/4.51
% 18.18/4.51 [1867] CLOSURE : ~iext(uri_rdf_first, skolem_BNODE_l223030, skolem_BNODE_l33131)
% 18.18/4.51
% 18.18/4.51 [1866] BETA_NOT_AND : ~(iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030))
% 18.18/4.51 -> [1868] ~iext(uri_rdf_first, skolem_BNODE_l212929, uri_ex_hasCousin)
% 18.18/4.51 -> [1869] ~iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)
% 18.18/4.51
% 18.18/4.51 [1869] CLOSURE : ~iext(uri_rdf_rest, skolem_BNODE_l212929, skolem_BNODE_l223030)
% 18.18/4.51
% 18.18/4.51 [1868] GAMMA_FORALL : ! [X25_25, Y26_26] : ((iext(skolem_BNODE_l33131, X25_25, Y26_26) <=> iext(uri_ex_hasFather, Y26_26, X25_25)))
% 18.18/4.51 -> [1870] (iext(skolem_BNODE_l33131, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))
% 18.18/4.51
% 18.18/4.51 [1870] BETA_EQUIV : (iext(skolem_BNODE_l33131, uri_ex_dave, uri_ex_alice) <=> iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave))
% 18.18/4.51 -> [1871] ~iext(skolem_BNODE_l33131, uri_ex_dave, uri_ex_alice), ~iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)
% 18.18/4.51 -> [1872] iext(skolem_BNODE_l33131, uri_ex_dave, uri_ex_alice), iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)
% 18.18/4.51
% 18.18/4.51 [1871] CLOSURE : ~iext(uri_ex_hasFather, uri_ex_alice, uri_ex_dave)
% 18.18/4.51
% 18.18/4.51 [1872] : ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.51 -> [1873] ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.51
% 18.18/4.51 [1873] GAMMA_FORALL : ! [P15_15, S116_16, P117_17, S218_18, P219_19] : (((((iext(uri_rdf_first, S116_16, P117_17) & iext(uri_rdf_rest, S116_16, S218_18)) & iext(uri_rdf_first, S218_18, P219_19)) & iext(uri_rdf_rest, S218_18, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P15_15, S116_16) <=> (((ip(P15_15) & ip(P117_17)) & ip(P219_19)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(P117_17, Y020_20, Y121_21) & iext(P219_19, Y121_21, Y222_22)) => iext(P15_15, Y020_20, Y222_22)))))))
% 18.18/4.51 -> [1874] ((((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))))
% 18.18/4.51
% 18.18/4.51 [1874] BETA_IMPLY : ((((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))))
% 18.18/4.51 -> [1875] ~(((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil))
% 18.18/4.51 -> [1876] (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22)))))
% 18.18/4.51
% 18.18/4.51 [1875] BETA_NOT_AND : ~(((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)) & iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil))
% 18.18/4.51 -> [1877] ~((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather))
% 18.18/4.51 -> [1878] ~iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)
% 18.18/4.51
% 18.18/4.51 [1877] BETA_NOT_AND : ~((iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)) & iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather))
% 18.18/4.51 -> [1881] ~(iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828))
% 18.18/4.51 -> [1882] ~iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)
% 18.18/4.51
% 18.18/4.51 [1882] CLOSURE : ~iext(uri_rdf_first, skolem_BNODE_l122828, uri_ex_hasFather)
% 18.18/4.51
% 18.18/4.51 [1881] BETA_NOT_AND : ~(iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin) & iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828))
% 18.18/4.51 -> [1960] ~iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)
% 18.18/4.51 -> [1961] ~iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)
% 18.18/4.51
% 18.18/4.51 [1960] CLOSURE : ~iext(uri_rdf_first, skolem_BNODE_l112727, uri_ex_hasCousin)
% 18.18/4.51
% 18.18/4.51 [1961] CLOSURE : ~iext(uri_rdf_rest, skolem_BNODE_l112727, skolem_BNODE_l122828)
% 18.18/4.51
% 18.18/4.51 [1878] CLOSURE : ~iext(uri_rdf_rest, skolem_BNODE_l122828, uri_rdf_nil)
% 18.18/4.51
% 18.18/4.51 [1876] BETA_EQUIV : (iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727) <=> (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22)))))
% 18.18/4.51 -> [2026] ~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727), ~(((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))
% 18.18/4.51 -> [2027] iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727), (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))
% 18.18/4.51
% 18.18/4.51 [2026] CLOSURE : ~iext(uri_owl_propertyChainAxiom, uri_ex_hasUncle, skolem_BNODE_l112727)
% 18.18/4.51
% 18.18/4.51 [2027] ALPHA_AND : (((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)) & ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22))))
% 18.18/4.51 -> [2028] ((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather)), ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22)))
% 18.18/4.51
% 18.18/4.51 [2028] ALPHA_AND : ((ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)) & ip(uri_ex_hasFather))
% 18.18/4.51 -> [2029] (ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin)), ip(uri_ex_hasFather)
% 18.18/4.51
% 18.18/4.51 [2029] ALPHA_AND : (ip(uri_ex_hasUncle) & ip(uri_ex_hasCousin))
% 18.18/4.51 -> [2030] ip(uri_ex_hasUncle), ip(uri_ex_hasCousin)
% 18.18/4.51
% 18.18/4.51 [2030] GAMMA_FORALL : ! [Y020_20, Y121_21, Y222_22] : (((iext(uri_ex_hasCousin, Y020_20, Y121_21) & iext(uri_ex_hasFather, Y121_21, Y222_22)) => iext(uri_ex_hasUncle, Y020_20, Y222_22)))
% 18.18/4.51 -> [2031] ((iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) => iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly))
% 18.18/4.51
% 18.18/4.51 [2031] BETA_IMPLY : ((iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)) => iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly))
% 18.18/4.51 -> [2032] ~(iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly))
% 18.18/4.51 -> [2033] iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [2032] BETA_NOT_AND : ~(iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob) & iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly))
% 18.18/4.51 -> [2034] ~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)
% 18.18/4.51 -> [2035] ~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [2034] CLOSURE : ~iext(uri_ex_hasCousin, uri_ex_alice, uri_ex_bob)
% 18.18/4.51
% 18.18/4.51 [2035] CLOSURE : ~iext(uri_ex_hasFather, uri_ex_bob, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 [2033] CLOSURE : iext(uri_ex_hasUncle, uri_ex_alice, uri_ex_charly)
% 18.18/4.51
% 18.18/4.51 % SZS output end Proof for theBenchmark.p
% 18.18/4.51 [4.151199s][1][Res] 48262 goroutines created
% 18.18/4.51 ==== Result ====
% 18.18/4.51 [4.151236s][1][Res] VALID
% 18.18/4.51 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------