TSTP Solution File: SEU080+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SEU080+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n007.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 15:59:17 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU080+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 01:42:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.52 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 0.19/0.52 (* PROOF-FOUND *)
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 (* BEGIN-PROOF *)
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 Theorem t161_funct_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (((relation C)/\(function C))->((((relation_inverse_image C A) = (relation_inverse_image C B))/\((subset A (relation_rng C))/\(subset B (relation_rng C))))->(A = B)))))).
% 0.19/0.52 Proof.
% 0.19/0.52 assert (zenon_L1_ : forall (zenon_TA_bm : zenon_U) (zenon_TB_bn : zenon_U), (forall B : zenon_U, ((zenon_TB_bn = B)<->((subset zenon_TB_bn B)/\(subset B zenon_TB_bn)))) -> (subset zenon_TA_bm zenon_TB_bn) -> (subset zenon_TB_bn zenon_TA_bm) -> (~(zenon_TA_bm = zenon_TB_bn)) -> False).
% 0.19/0.52 do 2 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H25.
% 0.19/0.52 generalize (zenon_H22 zenon_TA_bm). zenon_intro zenon_H28.
% 0.19/0.52 apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H2c; zenon_intro zenon_H2b | zenon_intro zenon_H2a; zenon_intro zenon_H29 ].
% 0.19/0.52 apply (zenon_notand_s _ _ zenon_H2b); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ].
% 0.19/0.52 exact (zenon_H2e zenon_H24).
% 0.19/0.52 exact (zenon_H2d zenon_H23).
% 0.19/0.52 apply zenon_H25. apply sym_equal. exact zenon_H2a.
% 0.19/0.52 (* end of lemma zenon_L1_ *)
% 0.19/0.52 assert (zenon_L2_ : forall (zenon_TA_bm : zenon_U) (zenon_TC_cb : zenon_U) (zenon_TB_bn : zenon_U), (forall x : zenon_U, (subset x x)) -> (forall B : zenon_U, (forall C : zenon_U, (((relation C)/\(function C))->(((subset (relation_inverse_image C zenon_TB_bn) (relation_inverse_image C B))/\(subset zenon_TB_bn (relation_rng C)))->(subset zenon_TB_bn B))))) -> (relation zenon_TC_cb) -> (function zenon_TC_cb) -> ((relation_inverse_image zenon_TC_cb zenon_TA_bm) = (relation_inverse_image zenon_TC_cb zenon_TB_bn)) -> (subset zenon_TB_bn (relation_rng zenon_TC_cb)) -> (subset zenon_TA_bm zenon_TB_bn) -> (~(zenon_TA_bm = zenon_TB_bn)) -> False).
% 0.19/0.52 do 3 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_H32 zenon_H33 zenon_H34 zenon_H23 zenon_H25.
% 0.19/0.52 generalize (zenon_H30 zenon_TA_bm). zenon_intro zenon_H36.
% 0.19/0.52 generalize (d10_xboole_0 zenon_TB_bn). zenon_intro zenon_H22.
% 0.19/0.52 generalize (zenon_H36 zenon_TC_cb). zenon_intro zenon_H37.
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ].
% 0.19/0.52 apply (zenon_notand_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 0.19/0.52 exact (zenon_H3b zenon_H31).
% 0.19/0.52 exact (zenon_H3a zenon_H32).
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3c | zenon_intro zenon_H24 ].
% 0.19/0.52 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ].
% 0.19/0.52 generalize (zenon_H2f (relation_inverse_image zenon_TC_cb zenon_TB_bn)). zenon_intro zenon_H3f.
% 0.19/0.52 cut ((subset (relation_inverse_image zenon_TC_cb zenon_TB_bn) (relation_inverse_image zenon_TC_cb zenon_TB_bn)) = (subset (relation_inverse_image zenon_TC_cb zenon_TB_bn) (relation_inverse_image zenon_TC_cb zenon_TA_bm))).
% 0.19/0.52 intro zenon_D_pnotp.
% 0.19/0.52 apply zenon_H3e.
% 0.19/0.52 rewrite <- zenon_D_pnotp.
% 0.19/0.52 exact zenon_H3f.
% 0.19/0.52 cut (((relation_inverse_image zenon_TC_cb zenon_TB_bn) = (relation_inverse_image zenon_TC_cb zenon_TA_bm))); [idtac | apply NNPP; zenon_intro zenon_H40].
% 0.19/0.52 cut (((relation_inverse_image zenon_TC_cb zenon_TB_bn) = (relation_inverse_image zenon_TC_cb zenon_TB_bn))); [idtac | apply NNPP; zenon_intro zenon_H41].
% 0.19/0.52 congruence.
% 0.19/0.52 apply zenon_H41. apply refl_equal.
% 0.19/0.52 apply zenon_H40. apply sym_equal. exact zenon_H33.
% 0.19/0.52 exact (zenon_H3d zenon_H34).
% 0.19/0.52 apply (zenon_L1_ zenon_TA_bm zenon_TB_bn); trivial.
% 0.19/0.52 (* end of lemma zenon_L2_ *)
% 0.19/0.52 apply NNPP. intro zenon_G.
% 0.19/0.52 elim (classic (forall x : zenon_U, (subset x x))); [ zenon_intro zenon_H2f | zenon_intro zenon_H42 ].
% 0.19/0.52 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (((relation C)/\(function C))->((((relation_inverse_image C A) = (relation_inverse_image C B))/\((subset A (relation_rng C))/\(subset B (relation_rng C))))->(A = B)))))) zenon_G); [ zenon_intro zenon_H43; idtac ].
% 0.19/0.52 elim zenon_H43. zenon_intro zenon_TA_bm. zenon_intro zenon_H44.
% 0.19/0.52 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((relation C)/\(function C))->((((relation_inverse_image C zenon_TA_bm) = (relation_inverse_image C B))/\((subset zenon_TA_bm (relation_rng C))/\(subset B (relation_rng C))))->(zenon_TA_bm = B))))) zenon_H44); [ zenon_intro zenon_H45; idtac ].
% 0.19/0.52 elim zenon_H45. zenon_intro zenon_TB_bn. zenon_intro zenon_H46.
% 0.19/0.52 apply (zenon_notallex_s (fun C : zenon_U => (((relation C)/\(function C))->((((relation_inverse_image C zenon_TA_bm) = (relation_inverse_image C zenon_TB_bn))/\((subset zenon_TA_bm (relation_rng C))/\(subset zenon_TB_bn (relation_rng C))))->(zenon_TA_bm = zenon_TB_bn)))) zenon_H46); [ zenon_intro zenon_H47; idtac ].
% 0.19/0.52 elim zenon_H47. zenon_intro zenon_TC_cb. zenon_intro zenon_H48.
% 0.19/0.52 apply (zenon_notimply_s _ _ zenon_H48). zenon_intro zenon_H4a. zenon_intro zenon_H49.
% 0.19/0.52 apply (zenon_notimply_s _ _ zenon_H49). zenon_intro zenon_H4b. zenon_intro zenon_H25.
% 0.19/0.52 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H33. zenon_intro zenon_H4c.
% 0.19/0.52 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4d. zenon_intro zenon_H34.
% 0.19/0.52 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H31. zenon_intro zenon_H32.
% 0.19/0.52 generalize (t158_funct_1 zenon_TB_bn). zenon_intro zenon_H30.
% 0.19/0.52 generalize (t158_funct_1 zenon_TA_bm). zenon_intro zenon_H4e.
% 0.19/0.52 generalize (zenon_H4e zenon_TB_bn). zenon_intro zenon_H4f.
% 0.19/0.52 generalize (zenon_H4f zenon_TC_cb). zenon_intro zenon_H50.
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_H50); [ zenon_intro zenon_H39 | zenon_intro zenon_H51 ].
% 0.19/0.52 apply (zenon_notand_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 0.19/0.52 exact (zenon_H3b zenon_H31).
% 0.19/0.52 exact (zenon_H3a zenon_H32).
% 0.19/0.52 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H52 | zenon_intro zenon_H23 ].
% 0.19/0.52 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ].
% 0.19/0.52 generalize (zenon_H2f (relation_inverse_image zenon_TC_cb zenon_TA_bm)). zenon_intro zenon_H55.
% 0.19/0.52 cut ((subset (relation_inverse_image zenon_TC_cb zenon_TA_bm) (relation_inverse_image zenon_TC_cb zenon_TA_bm)) = (subset (relation_inverse_image zenon_TC_cb zenon_TA_bm) (relation_inverse_image zenon_TC_cb zenon_TB_bn))).
% 0.19/0.52 intro zenon_D_pnotp.
% 0.19/0.52 apply zenon_H54.
% 0.19/0.52 rewrite <- zenon_D_pnotp.
% 0.19/0.52 exact zenon_H55.
% 0.19/0.52 cut (((relation_inverse_image zenon_TC_cb zenon_TA_bm) = (relation_inverse_image zenon_TC_cb zenon_TB_bn))); [idtac | apply NNPP; zenon_intro zenon_H56].
% 0.19/0.52 cut (((relation_inverse_image zenon_TC_cb zenon_TA_bm) = (relation_inverse_image zenon_TC_cb zenon_TA_bm))); [idtac | apply NNPP; zenon_intro zenon_H57].
% 0.19/0.52 congruence.
% 0.19/0.52 apply zenon_H57. apply refl_equal.
% 0.19/0.52 exact (zenon_H56 zenon_H33).
% 0.19/0.52 exact (zenon_H53 zenon_H4d).
% 0.19/0.52 apply (zenon_L2_ zenon_TA_bm zenon_TC_cb zenon_TB_bn); trivial.
% 0.19/0.52 apply zenon_H42. zenon_intro zenon_Tx_dk. apply NNPP. zenon_intro zenon_H59.
% 0.19/0.52 generalize (reflexivity_r1_tarski zenon_Tx_dk). zenon_intro zenon_H0.
% 0.19/0.52 generalize (zenon_H0 zenon_E). zenon_intro zenon_H5a.
% 0.19/0.52 exact (zenon_H59 zenon_H5a).
% 0.19/0.52 Qed.
% 0.19/0.52 % SZS output end Proof
% 0.19/0.52 (* END-PROOF *)
% 0.19/0.52 nodes searched: 408
% 0.19/0.52 max branch formulas: 251
% 0.19/0.52 proof nodes created: 45
% 0.19/0.52 formulas created: 2111
% 0.19/0.52
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