%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET923+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 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 : Tue Jul 19 05:45:02 EDT 2022 % Result : Theorem 0.13s 0.39s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET923+1 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.33 % Computer : n015.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 09:28:24 EDT 2022 % 0.13/0.33 % CPUTime : % 0.13/0.39 % SZS status Theorem % 0.13/0.39 (* PROOF-FOUND *) % 0.13/0.39 (* BEGIN-PROOF *) % 0.13/0.39 % SZS output start Proof % 0.13/0.39 1. ((set_difference T_0 (singleton T_1)) = (empty_set)) ((set_difference T_0 (singleton T_1)) != (empty_set)) ### Axiom % 0.13/0.39 2. (-. (subset T_0 (singleton T_1))) ((set_difference T_0 (singleton T_1)) = (empty_set)) ### Definition-Pseudo(subset) 1 % 0.13/0.39 3. (T_0 != (empty_set)) (T_0 = (empty_set)) ### Axiom % 0.13/0.39 4. (T_0 != (singleton T_1)) (T_0 = (singleton T_1)) ### Axiom % 0.13/0.39 5. ((T_0 = (empty_set)) \/ (T_0 = (singleton T_1))) (T_0 != (singleton T_1)) (T_0 != (empty_set)) ### Or 3 4 % 0.13/0.39 6. ((subset T_0 (singleton T_1)) <=> ((T_0 = (empty_set)) \/ (T_0 = (singleton T_1)))) (T_0 != (empty_set)) (T_0 != (singleton T_1)) ((set_difference T_0 (singleton T_1)) = (empty_set)) ### Equiv 2 5 % 0.13/0.39 7. (All B, ((subset T_0 (singleton B)) <=> ((T_0 = (empty_set)) \/ (T_0 = (singleton B))))) ((set_difference T_0 (singleton T_1)) = (empty_set)) (T_0 != (singleton T_1)) (T_0 != (empty_set)) ### All 6 % 0.13/0.39 8. (All A, (All B, ((subset A (singleton B)) <=> ((A = (empty_set)) \/ (A = (singleton B)))))) (T_0 != (empty_set)) (T_0 != (singleton T_1)) ((set_difference T_0 (singleton T_1)) = (empty_set)) ### All 7 % 0.13/0.39 9. (((set_difference T_0 (singleton T_1)) = (empty_set)) /\ ((T_0 != (empty_set)) /\ (T_0 != (singleton T_1)))) (All A, (All B, ((subset A (singleton B)) <=> ((A = (empty_set)) \/ (A = (singleton B)))))) ### ConjTree 8 % 0.13/0.39 10. (-. (-. (((set_difference T_0 (singleton T_1)) = (empty_set)) /\ ((T_0 != (empty_set)) /\ (T_0 != (singleton T_1)))))) (All A, (All B, ((subset A (singleton B)) <=> ((A = (empty_set)) \/ (A = (singleton B)))))) ### NotNot 9 % 0.13/0.39 11. (-. (All B, (-. (((set_difference T_0 (singleton B)) = (empty_set)) /\ ((T_0 != (empty_set)) /\ (T_0 != (singleton B))))))) (All A, (All B, ((subset A (singleton B)) <=> ((A = (empty_set)) \/ (A = (singleton B)))))) ### NotAllEx 10 % 0.13/0.39 12. (-. (All A, (All B, (-. (((set_difference A (singleton B)) = (empty_set)) /\ ((A != (empty_set)) /\ (A != (singleton B)))))))) (All A, (All B, ((subset A (singleton B)) <=> ((A = (empty_set)) \/ (A = (singleton B)))))) ### NotAllEx 11 % 0.13/0.39 % SZS output end Proof % 0.13/0.39 (* END-PROOF *) %------------------------------------------------------------------------------