%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SYN071+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n025.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 13:49:23 EDT 2022 % Result : Theorem 0.19s 0.50s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SYN071+1 : TPTP v8.1.0. Released v2.0.0. % 0.08/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n025.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jul 11 16:09:32 EDT 2022 % 0.13/0.33 % CPUTime : % 0.19/0.50 (* PROOF-FOUND *) % 0.19/0.50 % SZS status Theorem % 0.19/0.50 (* BEGIN-PROOF *) % 0.19/0.50 % SZS output start Proof % 0.19/0.50 Theorem pel48 : (((a) = (d))\/((b) = (c))). % 0.19/0.50 Proof. % 0.19/0.50 assert (zenon_L1_ : (~((a) = (a))) -> False). % 0.19/0.50 do 0 intro. intros zenon_H3. % 0.19/0.50 apply zenon_H3. apply refl_equal. % 0.19/0.50 (* end of lemma zenon_L1_ *) % 0.19/0.50 assert (zenon_L2_ : (~((c) = (c))) -> False). % 0.19/0.50 do 0 intro. intros zenon_H4. % 0.19/0.50 apply zenon_H4. apply refl_equal. % 0.19/0.50 (* end of lemma zenon_L2_ *) % 0.19/0.50 apply NNPP. intro zenon_G. % 0.19/0.50 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_H6. zenon_intro zenon_H5. % 0.19/0.50 apply (zenon_or_s _ _ pel48_1); [ zenon_intro zenon_H8 | zenon_intro zenon_H7 ]. % 0.19/0.50 apply (zenon_or_s _ _ pel48_2); [ zenon_intro zenon_Ha | zenon_intro zenon_H9 ]. % 0.19/0.50 elim (classic ((c) = (c))); [ zenon_intro zenon_Hb | zenon_intro zenon_H4 ]. % 0.19/0.50 cut (((c) = (c)) = ((b) = (c))). % 0.19/0.50 intro zenon_D_pnotp. % 0.19/0.50 apply zenon_H5. % 0.19/0.50 rewrite <- zenon_D_pnotp. % 0.19/0.50 exact zenon_Hb. % 0.19/0.50 cut (((c) = (c))); [idtac | apply NNPP; zenon_intro zenon_H4]. % 0.19/0.50 cut (((c) = (b))); [idtac | apply NNPP; zenon_intro zenon_Hc]. % 0.19/0.50 congruence. % 0.19/0.50 cut (((a) = (b)) = ((c) = (b))). % 0.19/0.50 intro zenon_D_pnotp. % 0.19/0.50 apply zenon_Hc. % 0.19/0.50 rewrite <- zenon_D_pnotp. % 0.19/0.50 exact zenon_H8. % 0.19/0.50 cut (((b) = (b))); [idtac | apply NNPP; zenon_intro zenon_Hd]. % 0.19/0.50 cut (((a) = (c))); [idtac | apply NNPP; zenon_intro zenon_He]. % 0.19/0.50 congruence. % 0.19/0.50 exact (zenon_He zenon_Ha). % 0.19/0.50 apply zenon_Hd. apply refl_equal. % 0.19/0.50 apply zenon_H4. apply refl_equal. % 0.19/0.50 apply zenon_H4. apply refl_equal. % 0.19/0.50 cut (((a) = (b)) = ((a) = (d))). % 0.19/0.50 intro zenon_D_pnotp. % 0.19/0.50 apply zenon_H6. % 0.19/0.50 rewrite <- zenon_D_pnotp. % 0.19/0.50 exact zenon_H8. % 0.19/0.50 cut (((b) = (d))); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 0.19/0.50 cut (((a) = (a))); [idtac | apply NNPP; zenon_intro zenon_H3]. % 0.19/0.50 congruence. % 0.19/0.50 apply zenon_H3. apply refl_equal. % 0.19/0.50 exact (zenon_Hf zenon_H9). % 0.19/0.50 apply (zenon_or_s _ _ pel48_2); [ zenon_intro zenon_Ha | zenon_intro zenon_H9 ]. % 0.19/0.50 cut (((c) = (d)) = ((a) = (d))). % 0.19/0.50 intro zenon_D_pnotp. % 0.19/0.50 apply zenon_H6. % 0.19/0.50 rewrite <- zenon_D_pnotp. % 0.19/0.50 exact zenon_H7. % 0.19/0.50 cut (((d) = (d))); [idtac | apply NNPP; zenon_intro zenon_H10]. % 0.19/0.50 cut (((c) = (a))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 0.19/0.50 congruence. % 0.19/0.50 elim (classic ((a) = (a))); [ zenon_intro zenon_H12 | zenon_intro zenon_H3 ]. % 0.19/0.50 cut (((a) = (a)) = ((c) = (a))). % 0.19/0.50 intro zenon_D_pnotp. % 0.19/0.50 apply zenon_H11. % 0.19/0.50 rewrite <- zenon_D_pnotp. % 0.19/0.50 exact zenon_H12. % 0.19/0.50 cut (((a) = (a))); [idtac | apply NNPP; zenon_intro zenon_H3]. % 0.19/0.50 cut (((a) = (c))); [idtac | apply NNPP; zenon_intro zenon_He]. % 0.19/0.50 congruence. % 0.19/0.50 exact (zenon_He zenon_Ha). % 0.19/0.50 apply zenon_H3. apply refl_equal. % 0.19/0.50 apply zenon_H3. apply refl_equal. % 0.19/0.50 apply zenon_H10. apply refl_equal. % 0.19/0.50 elim (classic ((c) = (c))); [ zenon_intro zenon_Hb | zenon_intro zenon_H4 ]. % 0.19/0.50 cut (((c) = (c)) = ((b) = (c))). % 0.19/0.50 intro zenon_D_pnotp. % 0.19/0.50 apply zenon_H5. % 0.19/0.50 rewrite <- zenon_D_pnotp. % 0.19/0.50 exact zenon_Hb. % 0.19/0.50 cut (((c) = (c))); [idtac | apply NNPP; zenon_intro zenon_H4]. % 0.19/0.50 cut (((c) = (b))); [idtac | apply NNPP; zenon_intro zenon_Hc]. % 0.19/0.50 congruence. % 0.19/0.50 cut (((c) = (d)) = ((c) = (b))). % 0.19/0.50 intro zenon_D_pnotp. % 0.19/0.50 apply zenon_Hc. % 0.19/0.50 rewrite <- zenon_D_pnotp. % 0.19/0.50 exact zenon_H7. % 0.19/0.50 cut (((d) = (b))); [idtac | apply NNPP; zenon_intro zenon_H13]. % 0.19/0.50 cut (((c) = (c))); [idtac | apply NNPP; zenon_intro zenon_H4]. % 0.19/0.50 congruence. % 0.19/0.50 apply zenon_H4. apply refl_equal. % 0.19/0.50 apply zenon_H13. apply sym_equal. exact zenon_H9. % 0.19/0.50 apply zenon_H4. apply refl_equal. % 0.19/0.50 apply zenon_H4. apply refl_equal. % 0.19/0.50 Qed. % 0.19/0.50 % SZS output end Proof % 0.19/0.50 (* END-PROOF *) % 0.19/0.50 nodes searched: 20 % 0.19/0.50 max branch formulas: 10 % 0.19/0.50 proof nodes created: 18 % 0.19/0.50 formulas created: 96 % 0.19/0.50 %------------------------------------------------------------------------------