TSTP Solution File: NUM388+1 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : NUM388+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 : n028.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 : Mon Jul 18 14:42:06 EDT 2022
% Result : Theorem 1.27s 1.44s
% Output : Proof 1.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM388+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Thu Jul 7 10:39:23 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.27/1.44 % SZS status Theorem
% 1.27/1.44 (* PROOF-FOUND *)
% 1.27/1.44 (* BEGIN-PROOF *)
% 1.27/1.44 % SZS output start Proof
% 1.27/1.44 1. (ordinal T_0) (-. (ordinal T_0)) ### Axiom
% 1.27/1.44 2. (empty T_1) (-. (empty T_1)) ### Axiom
% 1.27/1.44 3. (in T_2 T_0) (-. (in T_2 T_0)) ### Axiom
% 1.27/1.44 4. (T_1 != T_1) ### Refl(=)
% 1.27/1.44 5. (in T_3 T_2) (-. (in T_3 T_2)) ### Axiom
% 1.27/1.44 6. (in T_2 T_0) (-. (in T_2 T_0)) ### Axiom
% 1.27/1.44 7. (-. (subset T_2 T_0)) (subset T_2 T_0) ### Axiom
% 1.27/1.44 8. ((in T_2 T_0) => (subset T_2 T_0)) (-. (subset T_2 T_0)) (in T_2 T_0) ### Imply 6 7
% 1.27/1.44 9. (All B, ((in B T_0) => (subset B T_0))) (in T_2 T_0) (-. (subset T_2 T_0)) ### All 8
% 1.27/1.44 10. (-. (element T_2 (powerset T_0))) (element T_2 (powerset T_0)) ### Axiom
% 1.27/1.44 11. ((element T_2 (powerset T_0)) <=> (subset T_2 T_0)) (-. (element T_2 (powerset T_0))) (in T_2 T_0) (All B, ((in B T_0) => (subset B T_0))) ### Equiv 9 10
% 1.27/1.44 12. (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (All B, ((in B T_0) => (subset B T_0))) (in T_2 T_0) (-. (element T_2 (powerset T_0))) ### All 11
% 1.27/1.44 13. (-. (element T_3 T_0)) (element T_3 T_0) ### Axiom
% 1.27/1.44 14. (((in T_3 T_2) /\ (element T_2 (powerset T_0))) => (element T_3 T_0)) (-. (element T_3 T_0)) (in T_2 T_0) (All B, ((in B T_0) => (subset B T_0))) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_3 T_2) ### DisjTree 5 12 13
% 1.27/1.44 15. (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (in T_3 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (All B, ((in B T_0) => (subset B T_0))) (in T_2 T_0) (-. (element T_3 T_0)) ### All 14
% 1.27/1.44 16. (-. (empty T_0)) (empty T_0) ### Axiom
% 1.27/1.44 17. (-. (in T_3 T_0)) (in T_3 T_0) ### Axiom
% 1.27/1.44 18. ((element T_3 T_0) => ((empty T_0) \/ (in T_3 T_0))) (-. (in T_3 T_0)) (-. (empty T_0)) (in T_2 T_0) (All B, ((in B T_0) => (subset B T_0))) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_3 T_2) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) ### DisjTree 15 16 17
% 1.27/1.44 19. (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (in T_3 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (All B, ((in B T_0) => (subset B T_0))) (in T_2 T_0) (-. (empty T_0)) (-. (in T_3 T_0)) ### All 18
% 1.27/1.44 20. ((empty_set) != T_0) (T_0 = (empty_set)) ### Sym(=)
% 1.27/1.44 21. ((empty T_0) => (T_0 = (empty_set))) ((empty_set) != T_0) (-. (in T_3 T_0)) (in T_2 T_0) (All B, ((in B T_0) => (subset B T_0))) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_3 T_2) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) ### Imply 19 20
% 1.27/1.44 22. (All A, ((empty A) => (A = (empty_set)))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (in T_3 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (All B, ((in B T_0) => (subset B T_0))) (in T_2 T_0) (-. (in T_3 T_0)) ((empty_set) != T_0) ### All 21
% 1.27/1.44 23. (T_0 != T_1) (T_1 = (empty_set)) (-. (in T_3 T_0)) (in T_2 T_0) (All B, ((in B T_0) => (subset B T_0))) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_3 T_2) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All A, ((empty A) => (A = (empty_set)))) ### Trans-sym 4 22
% 1.27/1.44 24. (-. (subset T_0 T_1)) (All A, ((empty A) => (A = (empty_set)))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (in T_3 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (All B, ((in B T_0) => (subset B T_0))) (in T_2 T_0) (-. (in T_3 T_0)) (T_1 = (empty_set)) ### Refl(subset) 23
% 1.27/1.44 25. (-. (element T_0 (powerset T_1))) (element T_0 (powerset T_1)) ### Axiom
% 1.27/1.44 26. ((element T_0 (powerset T_1)) <=> (subset T_0 T_1)) (-. (element T_0 (powerset T_1))) (T_1 = (empty_set)) (-. (in T_3 T_0)) (in T_2 T_0) (All B, ((in B T_0) => (subset B T_0))) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_3 T_2) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All A, ((empty A) => (A = (empty_set)))) ### Equiv 24 25
% 1.27/1.44 27. (All B, ((element T_0 (powerset B)) <=> (subset T_0 B))) (All A, ((empty A) => (A = (empty_set)))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (in T_3 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (All B, ((in B T_0) => (subset B T_0))) (in T_2 T_0) (-. (in T_3 T_0)) (T_1 = (empty_set)) (-. (element T_0 (powerset T_1))) ### All 26
% 1.27/1.44 28. (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (-. (element T_0 (powerset T_1))) (T_1 = (empty_set)) (-. (in T_3 T_0)) (in T_2 T_0) (All B, ((in B T_0) => (subset B T_0))) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_3 T_2) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All A, ((empty A) => (A = (empty_set)))) ### All 27
% 1.27/1.44 29. (empty T_1) (-. (empty T_1)) ### Axiom
% 1.27/1.44 30. (-. ((in T_2 T_0) /\ ((element T_0 (powerset T_1)) /\ (empty T_1)))) (empty T_1) (All A, ((empty A) => (A = (empty_set)))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (in T_3 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (All B, ((in B T_0) => (subset B T_0))) (-. (in T_3 T_0)) (T_1 = (empty_set)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (in T_2 T_0) ### DisjTree 3 28 29
% 1.27/1.44 31. (All C, (-. ((in T_2 T_0) /\ ((element T_0 (powerset C)) /\ (empty C))))) (in T_2 T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (T_1 = (empty_set)) (-. (in T_3 T_0)) (All B, ((in B T_0) => (subset B T_0))) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_3 T_2) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All A, ((empty A) => (A = (empty_set)))) (empty T_1) ### All 30
% 1.27/1.44 32. ((empty T_1) => (T_1 = (empty_set))) (All A, ((empty A) => (A = (empty_set)))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (in T_3 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (All B, ((in B T_0) => (subset B T_0))) (-. (in T_3 T_0)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (in T_2 T_0) (All C, (-. ((in T_2 T_0) /\ ((element T_0 (powerset C)) /\ (empty C))))) (empty T_1) ### Imply 2 31
% 1.27/1.44 33. (empty T_1) (All C, (-. ((in T_2 T_0) /\ ((element T_0 (powerset C)) /\ (empty C))))) (in T_2 T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (-. (in T_3 T_0)) (All B, ((in B T_0) => (subset B T_0))) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_3 T_2) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All A, ((empty A) => (A = (empty_set)))) ### All 32
% 1.27/1.44 34. (All B, (All C, (-. ((in T_2 B) /\ ((element B (powerset C)) /\ (empty C)))))) (All A, ((empty A) => (A = (empty_set)))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (in T_3 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (All B, ((in B T_0) => (subset B T_0))) (-. (in T_3 T_0)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (in T_2 T_0) (empty T_1) ### All 33
% 1.27/1.44 35. (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (empty T_1) (in T_2 T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (-. (in T_3 T_0)) (All B, ((in B T_0) => (subset B T_0))) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_3 T_2) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All A, ((empty A) => (A = (empty_set)))) ### All 34
% 1.27/1.44 36. (All A, ((empty A) => (A = (empty_set)))) (All B, ((element T_3 B) => ((empty B) \/ (in T_3 B)))) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (in T_3 T_2) (All B, ((in B T_0) => (subset B T_0))) (-. (in T_3 T_0)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (in T_2 T_0) (empty T_1) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) ### All 35
% 1.29/1.46 37. (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (empty T_1) (in T_2 T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (-. (in T_3 T_0)) (All B, ((in B T_0) => (subset B T_0))) (in T_3 T_2) (All C, (((in T_3 T_2) /\ (element T_2 (powerset C))) => (element T_3 C))) (All A, ((empty A) => (A = (empty_set)))) ### All 36
% 1.29/1.46 38. (All B, (All C, (((in T_3 B) /\ (element B (powerset C))) => (element T_3 C)))) (All A, ((empty A) => (A = (empty_set)))) (in T_3 T_2) (All B, ((in B T_0) => (subset B T_0))) (-. (in T_3 T_0)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (in T_2 T_0) (empty T_1) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) ### All 37
% 1.29/1.46 39. (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (empty T_1) (in T_2 T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (-. (in T_3 T_0)) (All B, ((in B T_0) => (subset B T_0))) (in T_3 T_2) (All A, ((empty A) => (A = (empty_set)))) ### All 38
% 1.29/1.46 40. (epsilon_transitive T_0) (All A, ((empty A) => (A = (empty_set)))) (in T_3 T_2) (-. (in T_3 T_0)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (in T_2 T_0) (empty T_1) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) ### Definition-Pseudo(epsilon_transitive) 39
% 1.29/1.46 41. ((epsilon_transitive T_0) /\ (epsilon_connected T_0)) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (empty T_1) (in T_2 T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (-. (in T_3 T_0)) (in T_3 T_2) (All A, ((empty A) => (A = (empty_set)))) ### And 40
% 1.29/1.46 42. ((ordinal T_0) => ((epsilon_transitive T_0) /\ (epsilon_connected T_0))) (All A, ((empty A) => (A = (empty_set)))) (in T_3 T_2) (-. (in T_3 T_0)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (in T_2 T_0) (empty T_1) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (ordinal T_0) ### Imply 1 41
% 1.29/1.46 43. (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) (ordinal T_0) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (empty T_1) (in T_2 T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (-. (in T_3 T_0)) (in T_3 T_2) (All A, ((empty A) => (A = (empty_set)))) ### All 42
% 1.29/1.46 44. (Ex A, (empty A)) (All A, ((empty A) => (A = (empty_set)))) (in T_3 T_2) (-. (in T_3 T_0)) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (in T_2 T_0) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (ordinal T_0) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) ### Exists 43
% 1.29/1.46 45. (-. ((epsilon_transitive T_3) => (((in T_3 T_2) /\ (in T_2 T_0)) => (in T_3 T_0)))) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) (ordinal T_0) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((empty A) => (A = (empty_set)))) (Ex A, (empty A)) ### ConjTree 44
% 1.29/1.46 46. (-. (All C, ((epsilon_transitive C) => (((in C T_2) /\ (in T_2 T_0)) => (in C T_0))))) (Ex A, (empty A)) (All A, ((empty A) => (A = (empty_set)))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (ordinal T_0) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) ### NotAllEx 45
% 1.29/1.46 47. (-. ((ordinal T_0) => (All C, ((epsilon_transitive C) => (((in C T_2) /\ (in T_2 T_0)) => (in C T_0)))))) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((empty A) => (A = (empty_set)))) (Ex A, (empty A)) ### NotImply 46
% 1.29/1.46 48. (-. (All B, ((ordinal B) => (All C, ((epsilon_transitive C) => (((in C T_2) /\ (in T_2 B)) => (in C B))))))) (Ex A, (empty A)) (All A, ((empty A) => (A = (empty_set)))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) ### NotAllEx 47
% 1.29/1.46 49. (-. ((ordinal T_2) => (All B, ((ordinal B) => (All C, ((epsilon_transitive C) => (((in C T_2) /\ (in T_2 B)) => (in C B)))))))) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((empty A) => (A = (empty_set)))) (Ex A, (empty A)) ### NotImply 48
% 1.29/1.46 50. (-. (All A, ((ordinal A) => (All B, ((ordinal B) => (All C, ((epsilon_transitive C) => (((in C A) /\ (in A B)) => (in C B))))))))) (Ex A, (empty A)) (All A, ((empty A) => (A = (empty_set)))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (All A, ((ordinal A) => ((epsilon_transitive A) /\ (epsilon_connected A)))) ### NotAllEx 49
% 1.29/1.46 % SZS output end Proof
% 1.29/1.46 (* END-PROOF *)
%------------------------------------------------------------------------------