TSTP Solution File: SET020+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n020.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 06:32:35 EDT 2022
% Result : Theorem 6.79s 6.99s
% Output : Proof 6.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n020.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 : 600
% 0.12/0.33 % DateTime : Mon Jul 11 01:26:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 6.79/6.99 (* PROOF-FOUND *)
% 6.79/6.99 % SZS status Theorem
% 6.79/6.99 (* BEGIN-PROOF *)
% 6.79/6.99 % SZS output start Proof
% 6.79/6.99 Theorem unique_1st_and_2nd_in_pair_of_sets1 : (forall U : zenon_U, (forall V : zenon_U, (forall X : zenon_U, (((member U (universal_class))/\((member V (universal_class))/\(X = (ordered_pair U V))))->(((first X) = U)/\((second X) = V)))))).
% 6.79/6.99 Proof.
% 6.79/6.99 assert (zenon_L1_ : forall (zenon_TV_bu : zenon_U) (zenon_TU_bv : zenon_U) (zenon_TX_bw : zenon_U), (~(zenon_TX_bw = (ordered_pair zenon_TU_bv zenon_TV_bu))) -> (zenon_TX_bw = (unordered_pair (singleton zenon_TU_bv) (unordered_pair zenon_TU_bv (singleton zenon_TV_bu)))) -> False).
% 6.79/6.99 do 3 intro. intros zenon_H2c zenon_H2d.
% 6.79/6.99 generalize (ordered_pair_defn zenon_TU_bv). zenon_intro zenon_H31.
% 6.79/6.99 generalize (zenon_H31 zenon_TV_bu). zenon_intro zenon_H32.
% 6.79/6.99 apply (zenon_congruence_lr_s _ (fun zenon_Vi : _ => (~(zenon_TX_bw = zenon_Vi))) _ _ zenon_H2c zenon_H32). zenon_intro zenon_H33.
% 6.79/6.99 exact (zenon_H33 zenon_H2d).
% 6.79/6.99 (* end of lemma zenon_L1_ *)
% 6.79/6.99 assert (zenon_L2_ : forall (zenon_TV_bu : zenon_U) (zenon_TU_bv : zenon_U) (zenon_TX_bw : zenon_U), (~((first zenon_TX_bw) = (first (ordered_pair zenon_TU_bv zenon_TV_bu)))) -> (zenon_TX_bw = (unordered_pair (singleton zenon_TU_bv) (unordered_pair zenon_TU_bv (singleton zenon_TV_bu)))) -> False).
% 6.79/6.99 do 3 intro. intros zenon_H34 zenon_H2d.
% 6.79/6.99 cut ((zenon_TX_bw = (ordered_pair zenon_TU_bv zenon_TV_bu))); [idtac | apply NNPP; zenon_intro zenon_H2c].
% 6.79/6.99 congruence.
% 6.79/6.99 apply (zenon_L1_ zenon_TV_bu zenon_TU_bv zenon_TX_bw); trivial.
% 6.79/6.99 (* end of lemma zenon_L2_ *)
% 6.79/6.99 assert (zenon_L3_ : forall (zenon_TV_bu : zenon_U) (zenon_TU_bv : zenon_U) (zenon_TX_bw : zenon_U), (~((second zenon_TX_bw) = (second (ordered_pair zenon_TU_bv zenon_TV_bu)))) -> (zenon_TX_bw = (unordered_pair (singleton zenon_TU_bv) (unordered_pair zenon_TU_bv (singleton zenon_TV_bu)))) -> False).
% 6.79/6.99 do 3 intro. intros zenon_H35 zenon_H2d.
% 6.79/6.99 cut ((zenon_TX_bw = (ordered_pair zenon_TU_bv zenon_TV_bu))); [idtac | apply NNPP; zenon_intro zenon_H2c].
% 6.79/6.99 congruence.
% 6.79/6.99 apply (zenon_L1_ zenon_TV_bu zenon_TU_bv zenon_TX_bw); trivial.
% 6.79/6.99 (* end of lemma zenon_L3_ *)
% 6.79/6.99 apply NNPP. intro zenon_G.
% 6.79/6.99 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (forall X : zenon_U, (((member U (universal_class))/\((member V (universal_class))/\(X = (ordered_pair U V))))->(((first X) = U)/\((second X) = V)))))) zenon_G); [ zenon_intro zenon_H36; idtac ].
% 6.79/6.99 elim zenon_H36. zenon_intro zenon_TU_bv. zenon_intro zenon_H37.
% 6.79/6.99 apply (zenon_notallex_s (fun V : zenon_U => (forall X : zenon_U, (((member zenon_TU_bv (universal_class))/\((member V (universal_class))/\(X = (ordered_pair zenon_TU_bv V))))->(((first X) = zenon_TU_bv)/\((second X) = V))))) zenon_H37); [ zenon_intro zenon_H38; idtac ].
% 6.79/6.99 elim zenon_H38. zenon_intro zenon_TV_bu. zenon_intro zenon_H39.
% 6.79/6.99 apply (zenon_notallex_s (fun X : zenon_U => (((member zenon_TU_bv (universal_class))/\((member zenon_TV_bu (universal_class))/\(X = (ordered_pair zenon_TU_bv zenon_TV_bu))))->(((first X) = zenon_TU_bv)/\((second X) = zenon_TV_bu)))) zenon_H39); [ zenon_intro zenon_H3a; idtac ].
% 6.79/6.99 elim zenon_H3a. zenon_intro zenon_TX_bw. zenon_intro zenon_H3b.
% 6.79/6.99 apply (zenon_notimply_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c.
% 6.79/6.99 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H3f. zenon_intro zenon_H3e.
% 6.79/6.99 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H41. zenon_intro zenon_H40.
% 6.79/6.99 generalize (ordered_pair_defn zenon_TU_bv). zenon_intro zenon_H31.
% 6.79/6.99 generalize (zenon_H31 zenon_TV_bu). zenon_intro zenon_H32.
% 6.79/6.99 apply (zenon_congruence_lr_s _ (fun zenon_Vg : _ => (zenon_TX_bw = zenon_Vg)) _ _ zenon_H40 zenon_H32). zenon_intro zenon_H2d.
% 6.79/6.99 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ].
% 6.79/6.99 generalize (first_second zenon_TU_bv). zenon_intro zenon_H44.
% 6.79/6.99 generalize (zenon_H44 zenon_TV_bu). zenon_intro zenon_H45.
% 6.79/6.99 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 6.79/6.99 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ].
% 6.79/6.99 exact (zenon_H49 zenon_H3f).
% 6.79/6.99 exact (zenon_H48 zenon_H41).
% 6.79/6.99 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H4b. zenon_intro zenon_H4a.
% 6.79/6.99 cut (((first (ordered_pair zenon_TU_bv zenon_TV_bu)) = zenon_TU_bv) = ((first zenon_TX_bw) = zenon_TU_bv)).
% 6.79/6.99 intro zenon_D_pnotp.
% 6.79/6.99 apply zenon_H43.
% 6.79/6.99 rewrite <- zenon_D_pnotp.
% 6.79/6.99 exact zenon_H4b.
% 6.79/6.99 cut ((zenon_TU_bv = zenon_TU_bv)); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 6.79/6.99 cut (((first (ordered_pair zenon_TU_bv zenon_TV_bu)) = (first zenon_TX_bw))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 6.79/6.99 congruence.
% 6.79/6.99 elim (classic ((first zenon_TX_bw) = (first zenon_TX_bw))); [ zenon_intro zenon_H4e | zenon_intro zenon_H4f ].
% 6.79/6.99 cut (((first zenon_TX_bw) = (first zenon_TX_bw)) = ((first (ordered_pair zenon_TU_bv zenon_TV_bu)) = (first zenon_TX_bw))).
% 6.79/6.99 intro zenon_D_pnotp.
% 6.79/6.99 apply zenon_H4d.
% 6.79/6.99 rewrite <- zenon_D_pnotp.
% 6.79/6.99 exact zenon_H4e.
% 6.79/6.99 cut (((first zenon_TX_bw) = (first zenon_TX_bw))); [idtac | apply NNPP; zenon_intro zenon_H4f].
% 6.79/6.99 cut (((first zenon_TX_bw) = (first (ordered_pair zenon_TU_bv zenon_TV_bu)))); [idtac | apply NNPP; zenon_intro zenon_H34].
% 6.79/6.99 congruence.
% 6.79/6.99 apply (zenon_L2_ zenon_TV_bu zenon_TU_bv zenon_TX_bw); trivial.
% 6.79/6.99 apply zenon_H4f. apply refl_equal.
% 6.79/6.99 apply zenon_H4f. apply refl_equal.
% 6.79/6.99 apply zenon_H4c. apply refl_equal.
% 6.79/6.99 generalize (first_second zenon_TV_bu). zenon_intro zenon_H50.
% 6.79/6.99 generalize (first_second zenon_TU_bv). zenon_intro zenon_H44.
% 6.79/6.99 generalize (zenon_H50 zenon_TV_bu). zenon_intro zenon_H51.
% 6.79/6.99 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ].
% 6.79/6.99 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H48 | zenon_intro zenon_H48 ].
% 6.79/6.99 exact (zenon_H48 zenon_H41).
% 6.79/6.99 exact (zenon_H48 zenon_H41).
% 6.79/6.99 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H55. zenon_intro zenon_H54.
% 6.79/6.99 cut (((first (ordered_pair zenon_TV_bu zenon_TV_bu)) = zenon_TV_bu) = ((second zenon_TX_bw) = zenon_TV_bu)).
% 6.79/6.99 intro zenon_D_pnotp.
% 6.79/6.99 apply zenon_H42.
% 6.79/6.99 rewrite <- zenon_D_pnotp.
% 6.79/6.99 exact zenon_H55.
% 6.79/6.99 cut ((zenon_TV_bu = zenon_TV_bu)); [idtac | apply NNPP; zenon_intro zenon_H56].
% 6.79/6.99 cut (((first (ordered_pair zenon_TV_bu zenon_TV_bu)) = (second zenon_TX_bw))); [idtac | apply NNPP; zenon_intro zenon_H57].
% 6.79/6.99 congruence.
% 6.79/6.99 elim (classic ((second zenon_TX_bw) = (second zenon_TX_bw))); [ zenon_intro zenon_H58 | zenon_intro zenon_H59 ].
% 6.79/6.99 cut (((second zenon_TX_bw) = (second zenon_TX_bw)) = ((first (ordered_pair zenon_TV_bu zenon_TV_bu)) = (second zenon_TX_bw))).
% 6.79/6.99 intro zenon_D_pnotp.
% 6.79/6.99 apply zenon_H57.
% 6.79/6.99 rewrite <- zenon_D_pnotp.
% 6.79/6.99 exact zenon_H58.
% 6.79/6.99 cut (((second zenon_TX_bw) = (second zenon_TX_bw))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 6.79/6.99 cut (((second zenon_TX_bw) = (first (ordered_pair zenon_TV_bu zenon_TV_bu)))); [idtac | apply NNPP; zenon_intro zenon_H5a].
% 6.79/6.99 congruence.
% 6.79/6.99 generalize (zenon_H44 zenon_TV_bu). zenon_intro zenon_H45.
% 6.79/6.99 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 6.79/6.99 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ].
% 6.79/6.99 exact (zenon_H49 zenon_H3f).
% 6.79/6.99 exact (zenon_H48 zenon_H41).
% 6.79/6.99 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H4b. zenon_intro zenon_H4a.
% 6.79/6.99 cut (((second (ordered_pair zenon_TU_bv zenon_TV_bu)) = zenon_TV_bu) = ((second zenon_TX_bw) = (first (ordered_pair zenon_TV_bu zenon_TV_bu)))).
% 6.79/6.99 intro zenon_D_pnotp.
% 6.79/6.99 apply zenon_H5a.
% 6.79/6.99 rewrite <- zenon_D_pnotp.
% 6.79/6.99 exact zenon_H4a.
% 6.79/6.99 cut ((zenon_TV_bu = (first (ordered_pair zenon_TV_bu zenon_TV_bu)))); [idtac | apply NNPP; zenon_intro zenon_H5b].
% 6.79/6.99 cut (((second (ordered_pair zenon_TU_bv zenon_TV_bu)) = (second zenon_TX_bw))); [idtac | apply NNPP; zenon_intro zenon_H5c].
% 6.79/6.99 congruence.
% 6.79/6.99 elim (classic ((second zenon_TX_bw) = (second zenon_TX_bw))); [ zenon_intro zenon_H58 | zenon_intro zenon_H59 ].
% 6.79/6.99 cut (((second zenon_TX_bw) = (second zenon_TX_bw)) = ((second (ordered_pair zenon_TU_bv zenon_TV_bu)) = (second zenon_TX_bw))).
% 6.79/6.99 intro zenon_D_pnotp.
% 6.79/6.99 apply zenon_H5c.
% 6.79/6.99 rewrite <- zenon_D_pnotp.
% 6.79/6.99 exact zenon_H58.
% 6.79/6.99 cut (((second zenon_TX_bw) = (second zenon_TX_bw))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 6.79/6.99 cut (((second zenon_TX_bw) = (second (ordered_pair zenon_TU_bv zenon_TV_bu)))); [idtac | apply NNPP; zenon_intro zenon_H35].
% 6.79/6.99 congruence.
% 6.79/6.99 apply (zenon_L3_ zenon_TV_bu zenon_TU_bv zenon_TX_bw); trivial.
% 6.79/6.99 apply zenon_H59. apply refl_equal.
% 6.79/6.99 apply zenon_H59. apply refl_equal.
% 6.79/6.99 apply zenon_H5b. apply sym_equal. exact zenon_H55.
% 6.79/6.99 apply zenon_H59. apply refl_equal.
% 6.79/6.99 apply zenon_H59. apply refl_equal.
% 6.79/6.99 apply zenon_H56. apply refl_equal.
% 6.79/6.99 Qed.
% 6.79/6.99 % SZS output end Proof
% 6.79/6.99 (* END-PROOF *)
% 6.79/6.99 nodes searched: 278944
% 6.79/6.99 max branch formulas: 14761
% 6.79/6.99 proof nodes created: 12743
% 6.79/6.99 formulas created: 1046557
% 6.79/6.99
%------------------------------------------------------------------------------