%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET146+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n013.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 05:39:52 EDT 2022 % Result : Theorem 2.19s 2.38s % Output : Proof 2.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET146+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.34 % Computer : n013.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jul 10 00:43:14 EDT 2022 % 0.12/0.34 % CPUTime : % 2.19/2.38 % SZS status Theorem % 2.19/2.38 (* PROOF-FOUND *) % 2.19/2.38 (* BEGIN-PROOF *) % 2.19/2.38 % SZS output start Proof % 2.19/2.38 1. (T_0 != T_0) ### Refl(=) % 2.19/2.38 2. ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) ((intersection T_1 (empty_set)) != (intersection (empty_set) T_1)) ### Sym(=) % 2.19/2.38 3. (-. (member T_0 (intersection (empty_set) T_1))) (member T_0 (intersection T_1 (empty_set))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) ### P-NotP 1 2 % 2.19/2.38 4. (-. (member T_0 (empty_set))) (member T_0 (empty_set)) ### Axiom % 2.19/2.38 5. ((member T_0 (empty_set)) /\ (member T_0 T_1)) (-. (member T_0 (empty_set))) ### And 4 % 2.19/2.38 6. ((member T_0 (intersection (empty_set) T_1)) <=> ((member T_0 (empty_set)) /\ (member T_0 T_1))) (-. (member T_0 (empty_set))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (member T_0 (intersection T_1 (empty_set))) ### Equiv 3 5 % 2.19/2.38 7. (All D, ((member D (intersection (empty_set) T_1)) <=> ((member D (empty_set)) /\ (member D T_1)))) (member T_0 (intersection T_1 (empty_set))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (-. (member T_0 (empty_set))) ### All 6 % 2.19/2.38 8. (All C, (All D, ((member D (intersection (empty_set) C)) <=> ((member D (empty_set)) /\ (member D C))))) (-. (member T_0 (empty_set))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (member T_0 (intersection T_1 (empty_set))) ### All 7 % 2.19/2.38 9. (member T_0 (empty_set)) (-. (member T_0 (empty_set))) ### Axiom % 2.19/2.38 10. (All B, (-. (member B (empty_set)))) (member T_0 (empty_set)) ### All 9 % 2.19/2.38 11. (-. ((member T_0 (empty_set)) <=> (member T_0 (intersection T_1 (empty_set))))) (All B, (-. (member B (empty_set)))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (All C, (All D, ((member D (intersection (empty_set) C)) <=> ((member D (empty_set)) /\ (member D C))))) ### NotEquiv 8 10 % 2.19/2.38 12. (-. (All D, ((member D (empty_set)) <=> (member D (intersection T_1 (empty_set)))))) (All C, (All D, ((member D (intersection (empty_set) C)) <=> ((member D (empty_set)) /\ (member D C))))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (All B, (-. (member B (empty_set)))) ### NotAllEx 11 % 2.19/2.38 13. ((intersection T_1 (empty_set)) != (empty_set)) ((empty_set) = (intersection T_1 (empty_set))) ### Sym(=) % 2.19/2.38 14. (((empty_set) = (intersection T_1 (empty_set))) <=> (All D, ((member D (empty_set)) <=> (member D (intersection T_1 (empty_set)))))) ((intersection T_1 (empty_set)) != (empty_set)) (All B, (-. (member B (empty_set)))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (All C, (All D, ((member D (intersection (empty_set) C)) <=> ((member D (empty_set)) /\ (member D C))))) ### Equiv 12 13 % 2.19/2.38 15. (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) (All C, (All D, ((member D (intersection (empty_set) C)) <=> ((member D (empty_set)) /\ (member D C))))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (All B, (-. (member B (empty_set)))) ((intersection T_1 (empty_set)) != (empty_set)) ### All 14 % 2.19/2.38 16. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ((intersection T_1 (empty_set)) != (empty_set)) (All B, (-. (member B (empty_set)))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) ### All 15 % 2.19/2.38 17. (All C, ((intersection (empty_set) C) = (intersection C (empty_set)))) (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) (All B, (-. (member B (empty_set)))) ((intersection T_1 (empty_set)) != (empty_set)) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### All 16 % 2.19/2.38 18. (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ((intersection T_1 (empty_set)) != (empty_set)) (All B, (-. (member B (empty_set)))) (All C, ((intersection (empty_set) C) = (intersection C (empty_set)))) ### All 17 % 2.19/2.38 19. (All B, (All C, ((intersection B C) = (intersection C B)))) (All B, (-. (member B (empty_set)))) ((intersection T_1 (empty_set)) != (empty_set)) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ### All 18 % 2.19/2.38 20. (-. (All B, ((intersection B (empty_set)) = (empty_set)))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### NotAllEx 19 % 2.19/2.38 % SZS output end Proof % 2.19/2.38 (* END-PROOF *) %------------------------------------------------------------------------------