%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SWW245+1 : TPTP v8.1.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n018.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 01:31:26 EDT 2022 % Result : Theorem 5.11s 5.33s % Output : Proof 5.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SWW245+1 : TPTP v8.1.0. Released v5.2.0. % 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n018.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 Jun 6 06:21:04 EDT 2022 % 0.12/0.33 % CPUTime : % 5.11/5.33 % SZS status Theorem % 5.11/5.33 (* PROOF-FOUND *) % 5.11/5.33 (* BEGIN-PROOF *) % 5.11/5.33 % SZS output start Proof % 5.11/5.33 1. (class_Rings_Oidom (t_a)) (-. (class_Rings_Oidom (t_a))) ### Axiom % 5.11/5.33 2. (class_Rings_Oidom (t_a)) (-. (class_Rings_Oidom (t_a))) ### Axiom % 5.11/5.33 3. ((v_c____) != (c_Groups_Ozero__class_Ozero (t_a))) ((v_c____) = (c_Groups_Ozero__class_Ozero (t_a))) ### Axiom % 5.11/5.33 4. (-. (Ex B_k, (Ex B_a, ((B_a != (c_Groups_Ozero__class_Ozero (t_a))) /\ (Ex B_q, ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) = (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)))) /\ ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) != (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Nat_OSuc (c_Polynomial_Odegree (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)))))) /\ (All B_z, ((hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____))) B_z) = (hAPP (hAPP (c_Groups_Otimes__class_Otimes (t_a)) (hAPP (hAPP (c_Power_Opower__class_Opower (t_a)) B_z) B_k)) (hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) B_a B_q)) B_z))))))))))) (Ex B_k, (Ex B_a, ((B_a != (c_Groups_Ozero__class_Ozero (t_a))) /\ (Ex B_q, ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) = (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)))) /\ ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) != (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Nat_OSuc (c_Polynomial_Odegree (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)))))) /\ (All B_z, ((hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____))) B_z) = (hAPP (hAPP (c_Groups_Otimes__class_Otimes (t_a)) (hAPP (hAPP (c_Power_Opower__class_Opower (t_a)) B_z) B_k)) (hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) B_a B_q)) B_z)))))))))) ### Axiom % 5.11/5.33 5. ((class_Rings_Oidom (t_a)) => (((v_c____) != (c_Groups_Ozero__class_Ozero (t_a))) => (Ex B_k, (Ex B_a, ((B_a != (c_Groups_Ozero__class_Ozero (t_a))) /\ (Ex B_q, ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) = (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)))) /\ ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) != (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Nat_OSuc (c_Polynomial_Odegree (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)))))) /\ (All B_z, ((hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____))) B_z) = (hAPP (hAPP (c_Groups_Otimes__class_Otimes (t_a)) (hAPP (hAPP (c_Power_Opower__class_Opower (t_a)) B_z) B_k)) (hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) B_a B_q)) B_z)))))))))))) (-. (Ex B_k, (Ex B_a, ((B_a != (c_Groups_Ozero__class_Ozero (t_a))) /\ (Ex B_q, ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) = (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)))) /\ ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) != (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Nat_OSuc (c_Polynomial_Odegree (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)))))) /\ (All B_z, ((hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____))) B_z) = (hAPP (hAPP (c_Groups_Otimes__class_Otimes (t_a)) (hAPP (hAPP (c_Power_Opower__class_Opower (t_a)) B_z) B_k)) (hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) B_a B_q)) B_z))))))))))) ((v_c____) != (c_Groups_Ozero__class_Ozero (t_a))) (class_Rings_Oidom (t_a)) ### DisjTree 2 3 4 % 5.11/5.33 6. (-. (Ex B_k, (Ex B_a, ((B_a != (c_Groups_Ozero__class_Ozero (t_a))) /\ (Ex B_q, ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) = (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)))) /\ ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) != (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Nat_OSuc (c_Polynomial_Odegree (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)))))) /\ (All B_z, ((hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____))) B_z) = (hAPP (hAPP (c_Groups_Otimes__class_Otimes (t_a)) (hAPP (hAPP (c_Power_Opower__class_Opower (t_a)) B_z) B_k)) (hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) B_a B_q)) B_z))))))))))) (Ex B_k, (Ex B_a, ((B_a != (c_Groups_Ozero__class_Ozero (t_a))) /\ (Ex B_q, ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) = (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)))) /\ ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) != (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Nat_OSuc (c_Polynomial_Odegree (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)))))) /\ (All B_z, ((hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____))) B_z) = (hAPP (hAPP (c_Groups_Otimes__class_Otimes (t_a)) (hAPP (hAPP (c_Power_Opower__class_Opower (t_a)) B_z) B_k)) (hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) B_a B_q)) B_z)))))))))) ### Axiom % 5.11/5.33 7. ((class_Rings_Oidom (t_a)) => (((v_c____) = (c_Groups_Ozero__class_Ozero (t_a))) => (Ex B_k, (Ex B_a, ((B_a != (c_Groups_Ozero__class_Ozero (t_a))) /\ (Ex B_q, ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) = (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)))) /\ ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) != (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Nat_OSuc (c_Polynomial_Odegree (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)))))) /\ (All B_z, ((hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____))) B_z) = (hAPP (hAPP (c_Groups_Otimes__class_Otimes (t_a)) (hAPP (hAPP (c_Power_Opower__class_Opower (t_a)) B_z) B_k)) (hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) B_a B_q)) B_z)))))))))))) (-. (Ex B_k, (Ex B_a, ((B_a != (c_Groups_Ozero__class_Ozero (t_a))) /\ (Ex B_q, ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) = (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)))) /\ ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) != (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Nat_OSuc (c_Polynomial_Odegree (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)))))) /\ (All B_z, ((hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____))) B_z) = (hAPP (hAPP (c_Groups_Otimes__class_Otimes (t_a)) (hAPP (hAPP (c_Power_Opower__class_Opower (t_a)) B_z) B_k)) (hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) B_a B_q)) B_z))))))))))) ((class_Rings_Oidom (t_a)) => (((v_c____) != (c_Groups_Ozero__class_Ozero (t_a))) => (Ex B_k, (Ex B_a, ((B_a != (c_Groups_Ozero__class_Ozero (t_a))) /\ (Ex B_q, ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) = (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)))) /\ ((((c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)) != (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) => ((c_Nat_OSuc (c_Groups_Oplus__class_Oplus (tc_Nat_Onat) (c_If (tc_Nat_Onat) (c_fequal B_q (c_Groups_Ozero__class_Ozero (tc_Polynomial_Opoly (t_a)))) (c_Groups_Ozero__class_Ozero (tc_Nat_Onat)) (c_Nat_OSuc (c_Polynomial_Odegree (t_a) B_q))) B_k)) = (c_Nat_OSuc (c_Polynomial_Odegree (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____)))))) /\ (All B_z, ((hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) (v_c____) (v_cs____))) B_z) = (hAPP (hAPP (c_Groups_Otimes__class_Otimes (t_a)) (hAPP (hAPP (c_Power_Opower__class_Opower (t_a)) B_z) B_k)) (hAPP (c_Polynomial_Opoly (t_a) (c_Polynomial_OpCons (t_a) B_a B_q)) B_z)))))))))))) (class_Rings_Oidom (t_a)) ### DisjTree 1 5 6 % 5.11/5.33 % SZS output end Proof % 5.11/5.33 (* END-PROOF *) %------------------------------------------------------------------------------