TSTP Solution File: ALG211+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n017.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 14 18:06:16 EDT 2022
% Result : Theorem 5.74s 5.99s
% Output : Proof 5.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% 0.08/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n017.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 : Wed Jun 8 06:02:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.74/5.99 % SZS status Theorem
% 5.74/5.99 (* PROOF-FOUND *)
% 5.74/5.99 (* BEGIN-PROOF *)
% 5.74/5.99 % SZS output start Proof
% 5.74/5.99 1. (a_vector_subspace_of T_0 T_1) (-. (a_vector_subspace_of T_0 T_1)) ### Axiom
% 5.74/5.99 2. (-. (a_vector_space T_0)) (a_vector_space T_0) ### Axiom
% 5.74/5.99 3. ((a_vector_subspace_of T_0 T_1) => (a_vector_space T_0)) (-. (a_vector_space T_0)) (a_vector_subspace_of T_0 T_1) ### Imply 1 2
% 5.74/5.99 4. (All B, ((a_vector_subspace_of T_0 B) => (a_vector_space T_0))) (a_vector_subspace_of T_0 T_1) (-. (a_vector_space T_0)) ### All 3
% 5.74/5.99 5. (All A, (All B, ((a_vector_subspace_of A B) => (a_vector_space A)))) (-. (a_vector_space T_0)) (a_vector_subspace_of T_0 T_1) ### All 4
% 5.74/5.99 6. (a_vector_space T_1) (-. (a_vector_space T_1)) ### Axiom
% 5.74/5.99 7. (a_vector_subspace_of T_0 T_1) (-. (a_vector_subspace_of T_0 T_1)) ### Axiom
% 5.74/5.99 8. (basis_of T_2 T_0) (-. (basis_of T_2 T_0)) ### Axiom
% 5.74/5.99 9. (-. (a_subset_of T_2 (vec_to_class T_0))) (a_subset_of T_2 (vec_to_class T_0)) ### Axiom
% 5.74/5.99 10. ((lin_ind_subset T_2 T_0) /\ (a_subset_of T_2 (vec_to_class T_0))) (-. (a_subset_of T_2 (vec_to_class T_0))) ### And 9
% 5.74/5.99 11. ((basis_of T_2 T_0) => ((lin_ind_subset T_2 T_0) /\ (a_subset_of T_2 (vec_to_class T_0)))) (-. (a_subset_of T_2 (vec_to_class T_0))) (basis_of T_2 T_0) ### Imply 8 10
% 5.74/5.99 12. (All V, ((basis_of T_2 V) => ((lin_ind_subset T_2 V) /\ (a_subset_of T_2 (vec_to_class V))))) (basis_of T_2 T_0) (-. (a_subset_of T_2 (vec_to_class T_0))) ### All 11
% 5.74/5.99 13. (basis_of T_2 T_0) (-. (basis_of T_2 T_0)) ### Axiom
% 5.74/5.99 14. (-. (lin_ind_subset T_2 T_0)) (lin_ind_subset T_2 T_0) ### Axiom
% 5.74/5.99 15. ((lin_ind_subset T_2 T_0) /\ (a_subset_of T_2 (vec_to_class T_0))) (-. (lin_ind_subset T_2 T_0)) ### And 14
% 5.74/5.99 16. ((basis_of T_2 T_0) => ((lin_ind_subset T_2 T_0) /\ (a_subset_of T_2 (vec_to_class T_0)))) (-. (lin_ind_subset T_2 T_0)) (basis_of T_2 T_0) ### Imply 13 15
% 5.74/5.99 17. (All V, ((basis_of T_2 V) => ((lin_ind_subset T_2 V) /\ (a_subset_of T_2 (vec_to_class V))))) (basis_of T_2 T_0) (-. (lin_ind_subset T_2 T_0)) ### All 16
% 5.74/5.99 18. (-. (lin_ind_subset T_2 T_1)) (lin_ind_subset T_2 T_1) ### Axiom
% 5.74/5.99 19. ((lin_ind_subset T_2 T_0) <=> (lin_ind_subset T_2 T_1)) (-. (lin_ind_subset T_2 T_1)) (basis_of T_2 T_0) (All V, ((basis_of T_2 V) => ((lin_ind_subset T_2 V) /\ (a_subset_of T_2 (vec_to_class V))))) ### Equiv 17 18
% 5.74/5.99 20. (((a_vector_subspace_of T_0 T_1) /\ (a_subset_of T_2 (vec_to_class T_0))) => ((lin_ind_subset T_2 T_0) <=> (lin_ind_subset T_2 T_1))) (-. (lin_ind_subset T_2 T_1)) (basis_of T_2 T_0) (All V, ((basis_of T_2 V) => ((lin_ind_subset T_2 V) /\ (a_subset_of T_2 (vec_to_class V))))) (a_vector_subspace_of T_0 T_1) ### DisjTree 7 12 19
% 5.74/5.99 21. (All E, (((a_vector_subspace_of T_0 T_1) /\ (a_subset_of E (vec_to_class T_0))) => ((lin_ind_subset E T_0) <=> (lin_ind_subset E T_1)))) (a_vector_subspace_of T_0 T_1) (All V, ((basis_of T_2 V) => ((lin_ind_subset T_2 V) /\ (a_subset_of T_2 (vec_to_class V))))) (basis_of T_2 T_0) (-. (lin_ind_subset T_2 T_1)) ### All 20
% 5.74/5.99 22. (All V, (All E, (((a_vector_subspace_of T_0 V) /\ (a_subset_of E (vec_to_class T_0))) => ((lin_ind_subset E T_0) <=> (lin_ind_subset E V))))) (-. (lin_ind_subset T_2 T_1)) (basis_of T_2 T_0) (All V, ((basis_of T_2 V) => ((lin_ind_subset T_2 V) /\ (a_subset_of T_2 (vec_to_class V))))) (a_vector_subspace_of T_0 T_1) ### All 21
% 5.74/5.99 23. (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (a_vector_subspace_of T_0 T_1) (All V, ((basis_of T_2 V) => ((lin_ind_subset T_2 V) /\ (a_subset_of T_2 (vec_to_class V))))) (basis_of T_2 T_0) (-. (lin_ind_subset T_2 T_1)) ### All 22
% 5.74/5.99 24. (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) (-. (lin_ind_subset T_2 T_1)) (basis_of T_2 T_0) (a_vector_subspace_of T_0 T_1) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) ### All 23
% 5.74/5.99 25. (basis_of T_3 T_1) (-. (basis_of T_3 T_1)) ### Axiom
% 5.74/5.99 26. (basis_of (union T_2 T_4) T_1) (-. (basis_of (union T_2 T_4) T_1)) ### Axiom
% 5.74/5.99 27. (basis_of T_2 T_0) (-. (basis_of T_2 T_0)) ### Axiom
% 5.74/5.99 28. (-. ((basis_of (union T_2 T_4) T_1) /\ (basis_of T_2 T_0))) (basis_of T_2 T_0) (basis_of (union T_2 T_4) T_1) ### NotAnd 26 27
% 5.74/5.99 29. (-. (Ex F, ((basis_of (union T_2 F) T_1) /\ (basis_of T_2 T_0)))) (basis_of (union T_2 T_4) T_1) (basis_of T_2 T_0) ### NotExists 28
% 5.74/5.99 30. ((a_subset_of T_4 T_3) /\ (basis_of (union T_2 T_4) T_1)) (basis_of T_2 T_0) (-. (Ex F, ((basis_of (union T_2 F) T_1) /\ (basis_of T_2 T_0)))) ### And 29
% 5.74/5.99 31. (Ex U, ((a_subset_of U T_3) /\ (basis_of (union T_2 U) T_1))) (-. (Ex F, ((basis_of (union T_2 F) T_1) /\ (basis_of T_2 T_0)))) (basis_of T_2 T_0) ### Exists 30
% 5.74/5.99 32. (((lin_ind_subset T_2 T_1) /\ (basis_of T_3 T_1)) => (Ex U, ((a_subset_of U T_3) /\ (basis_of (union T_2 U) T_1)))) (-. (Ex F, ((basis_of (union T_2 F) T_1) /\ (basis_of T_2 T_0)))) (basis_of T_3 T_1) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (a_vector_subspace_of T_0 T_1) (basis_of T_2 T_0) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) ### DisjTree 24 25 31
% 5.74/5.99 33. (All V, (((lin_ind_subset T_2 V) /\ (basis_of T_3 V)) => (Ex U, ((a_subset_of U T_3) /\ (basis_of (union T_2 U) V))))) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) (basis_of T_2 T_0) (a_vector_subspace_of T_0 T_1) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (basis_of T_3 T_1) (-. (Ex F, ((basis_of (union T_2 F) T_1) /\ (basis_of T_2 T_0)))) ### All 32
% 5.74/5.99 34. (All T, (All V, (((lin_ind_subset T_2 V) /\ (basis_of T V)) => (Ex U, ((a_subset_of U T) /\ (basis_of (union T_2 U) V)))))) (-. (Ex F, ((basis_of (union T_2 F) T_1) /\ (basis_of T_2 T_0)))) (basis_of T_3 T_1) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (a_vector_subspace_of T_0 T_1) (basis_of T_2 T_0) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) ### All 33
% 5.74/5.99 35. (Ex B, (basis_of B T_1)) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) (basis_of T_2 T_0) (a_vector_subspace_of T_0 T_1) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (-. (Ex F, ((basis_of (union T_2 F) T_1) /\ (basis_of T_2 T_0)))) (All T, (All V, (((lin_ind_subset T_2 V) /\ (basis_of T V)) => (Ex U, ((a_subset_of U T) /\ (basis_of (union T_2 U) V)))))) ### Exists 34
% 5.74/5.99 36. ((a_vector_space T_1) => (Ex B, (basis_of B T_1))) (All T, (All V, (((lin_ind_subset T_2 V) /\ (basis_of T V)) => (Ex U, ((a_subset_of U T) /\ (basis_of (union T_2 U) V)))))) (-. (Ex F, ((basis_of (union T_2 F) T_1) /\ (basis_of T_2 T_0)))) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (a_vector_subspace_of T_0 T_1) (basis_of T_2 T_0) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) (a_vector_space T_1) ### Imply 6 35
% 5.74/5.99 37. (All A, ((a_vector_space A) => (Ex B, (basis_of B A)))) (a_vector_space T_1) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) (basis_of T_2 T_0) (a_vector_subspace_of T_0 T_1) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (-. (Ex F, ((basis_of (union T_2 F) T_1) /\ (basis_of T_2 T_0)))) (All T, (All V, (((lin_ind_subset T_2 V) /\ (basis_of T V)) => (Ex U, ((a_subset_of U T) /\ (basis_of (union T_2 U) V)))))) ### All 36
% 5.74/5.99 38. (All S, (All T, (All V, (((lin_ind_subset S V) /\ (basis_of T V)) => (Ex U, ((a_subset_of U T) /\ (basis_of (union S U) V))))))) (-. (Ex F, ((basis_of (union T_2 F) T_1) /\ (basis_of T_2 T_0)))) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (a_vector_subspace_of T_0 T_1) (basis_of T_2 T_0) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) (a_vector_space T_1) (All A, ((a_vector_space A) => (Ex B, (basis_of B A)))) ### All 37
% 5.74/6.00 39. (-. (Ex E, (Ex F, ((basis_of (union E F) T_1) /\ (basis_of E T_0))))) (All A, ((a_vector_space A) => (Ex B, (basis_of B A)))) (a_vector_space T_1) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) (basis_of T_2 T_0) (a_vector_subspace_of T_0 T_1) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (All S, (All T, (All V, (((lin_ind_subset S V) /\ (basis_of T V)) => (Ex U, ((a_subset_of U T) /\ (basis_of (union S U) V))))))) ### NotExists 38
% 5.74/6.00 40. (Ex B, (basis_of B T_0)) (All S, (All T, (All V, (((lin_ind_subset S V) /\ (basis_of T V)) => (Ex U, ((a_subset_of U T) /\ (basis_of (union S U) V))))))) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (a_vector_subspace_of T_0 T_1) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) (a_vector_space T_1) (All A, ((a_vector_space A) => (Ex B, (basis_of B A)))) (-. (Ex E, (Ex F, ((basis_of (union E F) T_1) /\ (basis_of E T_0))))) ### Exists 39
% 5.74/6.00 41. ((a_vector_space T_0) => (Ex B, (basis_of B T_0))) (-. (Ex E, (Ex F, ((basis_of (union E F) T_1) /\ (basis_of E T_0))))) (All A, ((a_vector_space A) => (Ex B, (basis_of B A)))) (a_vector_space T_1) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (All S, (All T, (All V, (((lin_ind_subset S V) /\ (basis_of T V)) => (Ex U, ((a_subset_of U T) /\ (basis_of (union S U) V))))))) (a_vector_subspace_of T_0 T_1) (All A, (All B, ((a_vector_subspace_of A B) => (a_vector_space A)))) ### Imply 5 40
% 5.74/6.00 42. (All A, (All B, ((a_vector_subspace_of A B) => (a_vector_space A)))) (a_vector_subspace_of T_0 T_1) (All S, (All T, (All V, (((lin_ind_subset S V) /\ (basis_of T V)) => (Ex U, ((a_subset_of U T) /\ (basis_of (union S U) V))))))) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) (a_vector_space T_1) (All A, ((a_vector_space A) => (Ex B, (basis_of B A)))) (-. (Ex E, (Ex F, ((basis_of (union E F) T_1) /\ (basis_of E T_0))))) ### All 41
% 5.74/6.00 43. (-. (((a_vector_subspace_of T_0 T_1) /\ (a_vector_space T_1)) => (Ex E, (Ex F, ((basis_of (union E F) T_1) /\ (basis_of E T_0)))))) (All A, ((a_vector_space A) => (Ex B, (basis_of B A)))) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (All S, (All T, (All V, (((lin_ind_subset S V) /\ (basis_of T V)) => (Ex U, ((a_subset_of U T) /\ (basis_of (union S U) V))))))) (All A, (All B, ((a_vector_subspace_of A B) => (a_vector_space A)))) ### ConjTree 42
% 5.74/6.00 44. (-. (All V, (((a_vector_subspace_of T_0 V) /\ (a_vector_space V)) => (Ex E, (Ex F, ((basis_of (union E F) V) /\ (basis_of E T_0))))))) (All A, (All B, ((a_vector_subspace_of A B) => (a_vector_space A)))) (All S, (All T, (All V, (((lin_ind_subset S V) /\ (basis_of T V)) => (Ex U, ((a_subset_of U T) /\ (basis_of (union S U) V))))))) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) (All A, ((a_vector_space A) => (Ex B, (basis_of B A)))) ### NotAllEx 43
% 5.74/6.00 45. (-. (All W, (All V, (((a_vector_subspace_of W V) /\ (a_vector_space V)) => (Ex E, (Ex F, ((basis_of (union E F) V) /\ (basis_of E W)))))))) (All A, ((a_vector_space A) => (Ex B, (basis_of B A)))) (All B, (All V, ((basis_of B V) => ((lin_ind_subset B V) /\ (a_subset_of B (vec_to_class V)))))) (All W, (All V, (All E, (((a_vector_subspace_of W V) /\ (a_subset_of E (vec_to_class W))) => ((lin_ind_subset E W) <=> (lin_ind_subset E V)))))) (All S, (All T, (All V, (((lin_ind_subset S V) /\ (basis_of T V)) => (Ex U, ((a_subset_of U T) /\ (basis_of (union S U) V))))))) (All A, (All B, ((a_vector_subspace_of A B) => (a_vector_space A)))) ### NotAllEx 44
% 5.74/6.00 % SZS output end Proof
% 5.74/6.00 (* END-PROOF *)
%------------------------------------------------------------------------------