TSTP Solution File: SWB023+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWB023+2 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n022.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 : 600s
% DateTime : Tue Jul 19 19:26:50 EDT 2022
% Result : Theorem 18.04s 18.24s
% Output : Proof 18.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWB023+2 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 1 03:30:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 18.04/18.24 (* PROOF-FOUND *)
% 18.04/18.24 % SZS status Theorem
% 18.04/18.24 (* BEGIN-PROOF *)
% 18.04/18.24 % SZS output start Proof
% 18.04/18.24 Theorem testcase_conclusion_fullish_023_Unique_List_Components : ((iext (uri_owl_sameAs) (uri_ex_w) (uri_ex_u))/\(iext (uri_owl_sameAs) (uri_ex_w) (uri_ex_v))).
% 18.04/18.24 Proof.
% 18.04/18.24 assert (zenon_L1_ : (~((uri_ex_u) = (uri_ex_u))) -> False).
% 18.04/18.24 do 0 intro. intros zenon_H6.
% 18.04/18.24 apply zenon_H6. apply refl_equal.
% 18.04/18.24 (* end of lemma zenon_L1_ *)
% 18.04/18.24 assert (zenon_L2_ : (~((uri_owl_sameAs) = (uri_owl_sameAs))) -> False).
% 18.04/18.24 do 0 intro. intros zenon_H7.
% 18.04/18.24 apply zenon_H7. apply refl_equal.
% 18.04/18.24 (* end of lemma zenon_L2_ *)
% 18.04/18.24 assert (zenon_L3_ : forall (zenon_TBNODE_o_l : zenon_U), (forall C : zenon_U, ((iext (uri_rdf_type) (uri_ex_w) C)<->(icext C (uri_ex_w)))) -> (iext (uri_rdf_type) (uri_ex_w) zenon_TBNODE_o_l) -> (~(icext zenon_TBNODE_o_l (uri_ex_w))) -> False).
% 18.04/18.24 do 1 intro. intros zenon_H8 zenon_H9 zenon_Ha.
% 18.04/18.24 generalize (zenon_H8 zenon_TBNODE_o_l). zenon_intro zenon_Hc.
% 18.04/18.24 apply (zenon_equiv_s _ _ zenon_Hc); [ zenon_intro zenon_He; zenon_intro zenon_Ha | zenon_intro zenon_H9; zenon_intro zenon_Hd ].
% 18.04/18.24 exact (zenon_He zenon_H9).
% 18.04/18.24 exact (zenon_Ha zenon_Hd).
% 18.04/18.24 (* end of lemma zenon_L3_ *)
% 18.04/18.24 assert (zenon_L4_ : forall (zenon_TBNODE_o_l : zenon_U) (zenon_TBNODE_l_u : zenon_U), (forall A1 : zenon_U, (((iext (uri_rdf_first) zenon_TBNODE_l_u A1)/\(iext (uri_rdf_rest) zenon_TBNODE_l_u (uri_rdf_nil)))->((iext (uri_owl_oneOf) zenon_TBNODE_o_l zenon_TBNODE_l_u)<->((ic zenon_TBNODE_o_l)/\(forall X : zenon_U, ((icext zenon_TBNODE_o_l X)<->(X = A1))))))) -> (iext (uri_rdf_first) zenon_TBNODE_l_u (uri_ex_u)) -> (iext (uri_rdf_rest) zenon_TBNODE_l_u (uri_rdf_nil)) -> (forall C : zenon_U, ((iext (uri_rdf_type) (uri_ex_w) C)<->(icext C (uri_ex_w)))) -> (iext (uri_rdf_type) (uri_ex_w) zenon_TBNODE_o_l) -> (~((uri_ex_u) = (uri_ex_w))) -> (iext (uri_owl_oneOf) zenon_TBNODE_o_l zenon_TBNODE_l_u) -> False).
% 18.04/18.24 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11 zenon_H8 zenon_H9 zenon_H12 zenon_H13.
% 18.04/18.24 generalize (zenon_Hf (uri_ex_u)). zenon_intro zenon_H15.
% 18.04/18.24 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ].
% 18.04/18.24 apply (zenon_notand_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 18.04/18.24 exact (zenon_H19 zenon_H10).
% 18.04/18.24 exact (zenon_H18 zenon_H11).
% 18.04/18.24 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H1c; zenon_intro zenon_H1b | zenon_intro zenon_H13; zenon_intro zenon_H1a ].
% 18.04/18.24 exact (zenon_H1c zenon_H13).
% 18.04/18.24 apply (zenon_and_s _ _ zenon_H1a). zenon_intro zenon_H1e. zenon_intro zenon_H1d.
% 18.04/18.24 generalize (zenon_H1d (uri_ex_w)). zenon_intro zenon_H1f.
% 18.04/18.24 apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_Ha; zenon_intro zenon_H21 | zenon_intro zenon_Hd; zenon_intro zenon_H20 ].
% 18.04/18.24 apply (zenon_L3_ zenon_TBNODE_o_l); trivial.
% 18.04/18.24 apply zenon_H12. apply sym_equal. exact zenon_H20.
% 18.04/18.24 (* end of lemma zenon_L4_ *)
% 18.04/18.24 assert (zenon_L5_ : forall (zenon_TBNODE_l_u : zenon_U) (zenon_TBNODE_o_l : zenon_U), (forall S1 : zenon_U, (forall A1 : zenon_U, (((iext (uri_rdf_first) S1 A1)/\(iext (uri_rdf_rest) S1 (uri_rdf_nil)))->((iext (uri_owl_oneOf) zenon_TBNODE_o_l S1)<->((ic zenon_TBNODE_o_l)/\(forall X : zenon_U, ((icext zenon_TBNODE_o_l X)<->(X = A1)))))))) -> (iext (uri_owl_oneOf) zenon_TBNODE_o_l zenon_TBNODE_l_u) -> (~((uri_ex_u) = (uri_ex_w))) -> (iext (uri_rdf_type) (uri_ex_w) zenon_TBNODE_o_l) -> (forall C : zenon_U, ((iext (uri_rdf_type) (uri_ex_w) C)<->(icext C (uri_ex_w)))) -> (iext (uri_rdf_rest) zenon_TBNODE_l_u (uri_rdf_nil)) -> (iext (uri_rdf_first) zenon_TBNODE_l_u (uri_ex_u)) -> False).
% 18.04/18.24 do 2 intro. intros zenon_H22 zenon_H13 zenon_H12 zenon_H9 zenon_H8 zenon_H11 zenon_H10.
% 18.04/18.24 generalize (zenon_H22 zenon_TBNODE_l_u). zenon_intro zenon_Hf.
% 18.04/18.24 apply (zenon_L4_ zenon_TBNODE_o_l zenon_TBNODE_l_u); trivial.
% 18.04/18.24 (* end of lemma zenon_L5_ *)
% 18.04/18.24 assert (zenon_L6_ : (~((uri_ex_v) = (uri_ex_v))) -> False).
% 18.04/18.24 do 0 intro. intros zenon_H23.
% 18.04/18.24 apply zenon_H23. apply refl_equal.
% 18.04/18.24 (* end of lemma zenon_L6_ *)
% 18.04/18.24 assert (zenon_L7_ : (forall C : zenon_U, ((iext (uri_rdf_type) (uri_rdf_first) C)<->(icext C (uri_rdf_first)))) -> (iext (uri_rdf_type) (uri_rdf_first) (uri_owl_FunctionalProperty)) -> (~(icext (uri_owl_FunctionalProperty) (uri_rdf_first))) -> False).
% 18.04/18.24 do 0 intro. intros zenon_H24 zenon_H25 zenon_H26.
% 18.04/18.24 generalize (zenon_H24 (uri_owl_FunctionalProperty)). zenon_intro zenon_H27.
% 18.04/18.24 apply (zenon_equiv_s _ _ zenon_H27); [ zenon_intro zenon_H29; zenon_intro zenon_H26 | zenon_intro zenon_H25; zenon_intro zenon_H28 ].
% 18.04/18.24 exact (zenon_H29 zenon_H25).
% 18.04/18.24 exact (zenon_H26 zenon_H28).
% 18.04/18.24 (* end of lemma zenon_L7_ *)
% 18.04/18.24 assert (zenon_L8_ : (~(icext (uri_owl_FunctionalProperty) (uri_rdf_first))) -> (iext (uri_rdf_type) (uri_rdf_first) (uri_owl_FunctionalProperty)) -> False).
% 18.04/18.24 do 0 intro. intros zenon_H26 zenon_H25.
% 18.04/18.24 generalize (rdfs_cext_def (uri_rdf_first)). zenon_intro zenon_H24.
% 18.04/18.24 apply (zenon_L7_); trivial.
% 18.04/18.24 (* end of lemma zenon_L8_ *)
% 18.04/18.24 assert (zenon_L9_ : forall (zenon_TBNODE_o_l : zenon_U) (zenon_TBNODE_l_u : zenon_U), (iext (uri_rdf_first) zenon_TBNODE_l_u (uri_ex_u)) -> (iext (uri_rdf_rest) zenon_TBNODE_l_u (uri_rdf_nil)) -> (iext (uri_rdf_type) (uri_ex_w) zenon_TBNODE_o_l) -> (~((uri_ex_u) = (uri_ex_w))) -> (iext (uri_owl_oneOf) zenon_TBNODE_o_l zenon_TBNODE_l_u) -> (forall S1 : zenon_U, (forall A1 : zenon_U, (((iext (uri_rdf_first) S1 A1)/\(iext (uri_rdf_rest) S1 (uri_rdf_nil)))->((iext (uri_owl_oneOf) zenon_TBNODE_o_l S1)<->((ic zenon_TBNODE_o_l)/\(forall X : zenon_U, ((icext zenon_TBNODE_o_l X)<->(X = A1)))))))) -> False).
% 18.04/18.24 do 2 intro. intros zenon_H10 zenon_H11 zenon_H9 zenon_H12 zenon_H13 zenon_H22.
% 18.04/18.24 generalize (rdfs_cext_def (uri_ex_w)). zenon_intro zenon_H8.
% 18.04/18.24 apply (zenon_L5_ zenon_TBNODE_l_u zenon_TBNODE_o_l); trivial.
% 18.04/18.24 (* end of lemma zenon_L9_ *)
% 18.04/18.24 assert (zenon_L10_ : forall (zenon_TBNODE_o_l : zenon_U) (zenon_TBNODE_l_u : zenon_U), (~(iext (uri_owl_sameAs) (uri_ex_w) (uri_ex_v))) -> (iext (uri_owl_sameAs) (uri_ex_v) (uri_ex_v)) -> (iext (uri_rdf_first) zenon_TBNODE_l_u (uri_ex_u)) -> (iext (uri_rdf_rest) zenon_TBNODE_l_u (uri_rdf_nil)) -> (iext (uri_rdf_type) (uri_ex_w) zenon_TBNODE_o_l) -> (iext (uri_owl_oneOf) zenon_TBNODE_o_l zenon_TBNODE_l_u) -> (forall S1 : zenon_U, (forall A1 : zenon_U, (((iext (uri_rdf_first) S1 A1)/\(iext (uri_rdf_rest) S1 (uri_rdf_nil)))->((iext (uri_owl_oneOf) zenon_TBNODE_o_l S1)<->((ic zenon_TBNODE_o_l)/\(forall X : zenon_U, ((icext zenon_TBNODE_o_l X)<->(X = A1)))))))) -> ((uri_ex_v) = (uri_ex_u)) -> False).
% 18.04/18.24 do 2 intro. intros zenon_H2a zenon_H2b zenon_H10 zenon_H11 zenon_H9 zenon_H13 zenon_H22 zenon_H2c.
% 18.04/18.24 cut ((iext (uri_owl_sameAs) (uri_ex_v) (uri_ex_v)) = (iext (uri_owl_sameAs) (uri_ex_w) (uri_ex_v))).
% 18.04/18.24 intro zenon_D_pnotp.
% 18.04/18.24 apply zenon_H2a.
% 18.04/18.24 rewrite <- zenon_D_pnotp.
% 18.04/18.24 exact zenon_H2b.
% 18.04/18.24 cut (((uri_ex_v) = (uri_ex_v))); [idtac | apply NNPP; zenon_intro zenon_H23].
% 18.04/18.24 cut (((uri_ex_v) = (uri_ex_w))); [idtac | apply NNPP; zenon_intro zenon_H2d].
% 18.04/18.24 cut (((uri_owl_sameAs) = (uri_owl_sameAs))); [idtac | apply NNPP; zenon_intro zenon_H7].
% 18.04/18.24 congruence.
% 18.04/18.24 apply zenon_H7. apply refl_equal.
% 18.04/18.24 cut (((uri_ex_v) = (uri_ex_u)) = ((uri_ex_v) = (uri_ex_w))).
% 18.04/18.24 intro zenon_D_pnotp.
% 18.04/18.24 apply zenon_H2d.
% 18.04/18.24 rewrite <- zenon_D_pnotp.
% 18.04/18.24 exact zenon_H2c.
% 18.04/18.24 cut (((uri_ex_u) = (uri_ex_w))); [idtac | apply NNPP; zenon_intro zenon_H12].
% 18.04/18.24 cut (((uri_ex_v) = (uri_ex_v))); [idtac | apply NNPP; zenon_intro zenon_H23].
% 18.04/18.24 congruence.
% 18.04/18.24 apply zenon_H23. apply refl_equal.
% 18.04/18.24 apply (zenon_L9_ zenon_TBNODE_o_l zenon_TBNODE_l_u); trivial.
% 18.04/18.24 apply zenon_H23. apply refl_equal.
% 18.04/18.24 (* end of lemma zenon_L10_ *)
% 18.04/18.24 apply NNPP. intro zenon_G.
% 18.04/18.24 elim testcase_premise_fullish_023_Unique_List_Components. zenon_intro zenon_TBNODE_o_l. zenon_intro zenon_H2e.
% 18.04/18.24 elim zenon_H2e. zenon_intro zenon_TBNODE_l_u. zenon_intro zenon_H2f.
% 18.04/18.24 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H25. zenon_intro zenon_H30.
% 18.04/18.24 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H9. zenon_intro zenon_H31.
% 18.04/18.24 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H33. zenon_intro zenon_H32.
% 18.04/18.24 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H13. zenon_intro zenon_H34.
% 18.04/18.24 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H10. zenon_intro zenon_H35.
% 18.04/18.24 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H36. zenon_intro zenon_H11.
% 18.04/18.24 apply (zenon_notand_s _ _ zenon_G); [ zenon_intro zenon_H37 | zenon_intro zenon_H2a ].
% 18.04/18.24 generalize (owl_eqdis_sameas (uri_ex_u)). zenon_intro zenon_H38.
% 18.04/18.24 generalize (zenon_H38 (uri_ex_u)). zenon_intro zenon_H39.
% 18.04/18.24 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H3c; zenon_intro zenon_H6 | zenon_intro zenon_H3b; zenon_intro zenon_H3a ].
% 18.04/18.24 apply zenon_H6. apply refl_equal.
% 18.04/18.24 generalize (owl_enum_class_001 zenon_TBNODE_o_l). zenon_intro zenon_H22.
% 18.04/18.24 generalize (rdfs_cext_def (uri_ex_w)). zenon_intro zenon_H8.
% 18.04/18.24 cut ((iext (uri_owl_sameAs) (uri_ex_u) (uri_ex_u)) = (iext (uri_owl_sameAs) (uri_ex_w) (uri_ex_u))).
% 18.04/18.24 intro zenon_D_pnotp.
% 18.04/18.24 apply zenon_H37.
% 18.04/18.24 rewrite <- zenon_D_pnotp.
% 18.04/18.24 exact zenon_H3b.
% 18.04/18.24 cut (((uri_ex_u) = (uri_ex_u))); [idtac | apply NNPP; zenon_intro zenon_H6].
% 18.04/18.24 cut (((uri_ex_u) = (uri_ex_w))); [idtac | apply NNPP; zenon_intro zenon_H12].
% 18.04/18.24 cut (((uri_owl_sameAs) = (uri_owl_sameAs))); [idtac | apply NNPP; zenon_intro zenon_H7].
% 18.04/18.24 congruence.
% 18.04/18.24 apply zenon_H7. apply refl_equal.
% 18.04/18.24 apply (zenon_L5_ zenon_TBNODE_l_u zenon_TBNODE_o_l); trivial.
% 18.04/18.24 apply zenon_H6. apply refl_equal.
% 18.04/18.24 generalize (owl_eqdis_sameas (uri_ex_v)). zenon_intro zenon_H3d.
% 18.04/18.24 generalize (zenon_H3d (uri_ex_v)). zenon_intro zenon_H3e.
% 18.04/18.24 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H40; zenon_intro zenon_H23 | zenon_intro zenon_H2b; zenon_intro zenon_H3f ].
% 18.04/18.24 apply zenon_H23. apply refl_equal.
% 18.04/18.24 generalize (owl_enum_class_001 zenon_TBNODE_o_l). zenon_intro zenon_H22.
% 18.04/18.24 generalize (owl_char_functional (uri_rdf_first)). zenon_intro zenon_H41.
% 18.04/18.24 apply (zenon_equiv_s _ _ zenon_H41); [ zenon_intro zenon_H26; zenon_intro zenon_H43 | zenon_intro zenon_H28; zenon_intro zenon_H42 ].
% 18.04/18.24 apply (zenon_L8_); trivial.
% 18.04/18.24 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H45. zenon_intro zenon_H44.
% 18.04/18.24 generalize (zenon_H44 zenon_TBNODE_l_u). zenon_intro zenon_H46.
% 18.04/18.24 generalize (zenon_H46 (uri_ex_v)). zenon_intro zenon_H47.
% 18.04/18.24 generalize (zenon_H47 (uri_ex_u)). zenon_intro zenon_H48.
% 18.04/18.24 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H49 | zenon_intro zenon_H2c ].
% 18.04/18.24 apply (zenon_notand_s _ _ zenon_H49); [ zenon_intro zenon_H4a | zenon_intro zenon_H19 ].
% 18.04/18.24 exact (zenon_H4a zenon_H36).
% 18.04/18.24 exact (zenon_H19 zenon_H10).
% 18.04/18.24 apply (zenon_L10_ zenon_TBNODE_o_l zenon_TBNODE_l_u); trivial.
% 18.04/18.24 Qed.
% 18.04/18.24 % SZS output end Proof
% 18.04/18.24 (* END-PROOF *)
% 18.04/18.24 nodes searched: 756930
% 18.04/18.24 max branch formulas: 4356
% 18.04/18.24 proof nodes created: 22974
% 18.04/18.24 formulas created: 1366935
% 18.04/18.24
%------------------------------------------------------------------------------