%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL181+1 : TPTP v9.3.1. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n003.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:31:50 PM UTC 2026 % Result : Theorem 0.09s 0.44s % Output : Proof 0.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL181+1 : TPTP v9.3.1. Released v2.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.09/0.36 % Computer : n003.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Fri Sep 4 23:23:35 UTC 2026 % 0.09/0.36 % CPUTime : % 0.09/0.44 (* PROOF-FOUND *) % 0.09/0.44 % SZS status Theorem % 0.09/0.44 (* BEGIN-PROOF *) % 0.09/0.44 % SZS output start Proof % 0.09/0.44 Theorem pel4 : (((~(p))->(q))<->((~(q))->(p))). % 0.09/0.44 Proof. % 0.09/0.44 assert (zenon_L1_ : (~(q)) -> (q) -> False). % 0.09/0.44 do 0 intro. intros zenon_H1 zenon_H2. % 0.09/0.44 exact (zenon_H1 zenon_H2). % 0.09/0.44 (* end of lemma zenon_L1_ *) % 0.09/0.44 assert (zenon_L2_ : (~(p)) -> (p) -> False). % 0.09/0.44 do 0 intro. intros zenon_H3 zenon_H4. % 0.09/0.44 exact (zenon_H3 zenon_H4). % 0.09/0.44 (* end of lemma zenon_L2_ *) % 0.09/0.44 apply NNPP. intro zenon_G. % 0.09/0.44 apply (zenon_notequiv_s _ _ zenon_G); [ zenon_intro zenon_H8; zenon_intro zenon_H7 | zenon_intro zenon_H6; zenon_intro zenon_H5 ]. % 0.09/0.44 apply (zenon_notimply_s _ _ zenon_H8). zenon_intro zenon_H3. zenon_intro zenon_H1. % 0.09/0.44 apply (zenon_imply_s _ _ zenon_H7); [ zenon_intro zenon_H9 | zenon_intro zenon_H4 ]. % 0.09/0.44 exact (zenon_H9 zenon_H1). % 0.09/0.44 exact (zenon_H3 zenon_H4). % 0.09/0.44 apply (zenon_notimply_s _ _ zenon_H5). zenon_intro zenon_H1. zenon_intro zenon_H3. % 0.09/0.44 apply (zenon_imply_s _ _ zenon_H6); [ zenon_intro zenon_Ha | zenon_intro zenon_H2 ]. % 0.09/0.44 exact (zenon_Ha zenon_H3). % 0.09/0.44 exact (zenon_H1 zenon_H2). % 0.09/0.44 Qed. % 0.09/0.44 % SZS output end Proof % 0.09/0.44 (* END-PROOF *) % 0.09/0.44 nodes searched: 9 % 0.09/0.44 max branch formulas: 7 % 0.09/0.44 proof nodes created: 9 % 0.09/0.44 formulas created: 61 % 0.09/0.44 %------------------------------------------------------------------------------