%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SYN321+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n015.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 : Thu Jul 21 13:51:03 EDT 2022 % Result : Theorem 0.18s 0.48s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYN321+1 : TPTP v8.1.0. Released v2.0.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n015.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 : Tue Jul 12 02:40:39 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.48 (* PROOF-FOUND *) % 0.18/0.48 % SZS status Theorem % 0.18/0.48 (* BEGIN-PROOF *) % 0.18/0.48 % SZS output start Proof % 0.18/0.48 Theorem church_46_3_2 : (exists X : zenon_U, (exists Y : zenon_U, (((exists Z : zenon_U, (big_f X Z))->(forall Z : zenon_U, (big_g X Z)))->((forall Z : zenon_U, ((big_g Z Z)->(big_f Z Y)))->((big_f X Y)<->(forall Z : zenon_U, (big_g X Z))))))). % 0.18/0.48 Proof. % 0.18/0.48 assert (zenon_L1_ : (forall Z : zenon_U, (big_g zenon_E Z)) -> (~(big_f zenon_E zenon_E)) -> (forall Z : zenon_U, ((big_g Z Z)->(big_f Z zenon_E))) -> False). % 0.18/0.48 do 0 intro. intros zenon_H3 zenon_H4 zenon_H5. % 0.18/0.48 generalize (zenon_H3 zenon_E). zenon_intro zenon_H6. % 0.18/0.48 generalize (zenon_H5 zenon_E). zenon_intro zenon_H7. % 0.18/0.48 apply (zenon_imply_s _ _ zenon_H7); [ zenon_intro zenon_H9 | zenon_intro zenon_H8 ]. % 0.18/0.48 exact (zenon_H9 zenon_H6). % 0.18/0.48 exact (zenon_H4 zenon_H8). % 0.18/0.48 (* end of lemma zenon_L1_ *) % 0.18/0.48 apply NNPP. intro zenon_G. % 0.18/0.48 apply zenon_G. exists zenon_E. apply NNPP. zenon_intro zenon_Ha. % 0.18/0.48 apply zenon_Ha. exists zenon_E. apply NNPP. zenon_intro zenon_Hb. % 0.18/0.48 apply (zenon_notimply_s _ _ zenon_Hb). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 0.18/0.49 apply (zenon_notimply_s _ _ zenon_Hc). zenon_intro zenon_H5. zenon_intro zenon_He. % 0.18/0.49 apply (zenon_imply_s _ _ zenon_Hd); [ zenon_intro zenon_Hf | zenon_intro zenon_H3 ]. % 0.18/0.49 apply (zenon_notequiv_s _ _ zenon_He); [ zenon_intro zenon_H4; zenon_intro zenon_H3 | zenon_intro zenon_H8; zenon_intro zenon_H10 ]. % 0.18/0.49 apply (zenon_L1_); trivial. % 0.18/0.49 apply zenon_Hf. exists zenon_E. apply NNPP. zenon_intro zenon_H4. % 0.18/0.49 exact (zenon_H4 zenon_H8). % 0.18/0.49 apply (zenon_notequiv_s _ _ zenon_He); [ zenon_intro zenon_H4; zenon_intro zenon_H3 | zenon_intro zenon_H8; zenon_intro zenon_H10 ]. % 0.18/0.49 apply (zenon_L1_); trivial. % 0.18/0.49 exact (zenon_H10 zenon_H3). % 0.18/0.49 Qed. % 0.18/0.49 % SZS output end Proof % 0.18/0.49 (* END-PROOF *) % 0.18/0.49 nodes searched: 109 % 0.18/0.49 max branch formulas: 46 % 0.18/0.49 proof nodes created: 35 % 0.18/0.49 formulas created: 404 % 0.18/0.49 %------------------------------------------------------------------------------