TSTP Solution File: SWW245+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% 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 *)
%------------------------------------------------------------------------------