%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SWV164+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n003.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 : Wed Jul 20 21:50:13 EDT 2022 % Result : Theorem 7.05s 7.23s % Output : Proof 7.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SWV164+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.04/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.14/0.35 % Computer : n003.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Thu Jun 16 01:15:26 EDT 2022 % 0.14/0.35 % CPUTime : % 7.05/7.23 % SZS status Theorem % 7.05/7.23 (* PROOF-FOUND *) % 7.05/7.23 (* BEGIN-PROOF *) % 7.05/7.23 % SZS output start Proof % 7.05/7.23 1. (gt (succ T_0) (n0)) (-. (gt (succ T_0) (n0))) ### Axiom % 7.05/7.23 2. (-. (leq (n0) T_0)) (gt (succ T_0) (n0)) ### Definition-Pseudo(leq) 1 % 7.05/7.23 3. ((succ (n0)) = (n1)) ((n1) != (succ (n0))) ### Sym(=) % 7.05/7.23 4. ((succ (n1)) != (succ (succ (n0)))) ((succ (n0)) = (n1)) ### NotEqual 3 % 7.05/7.23 5. ((n2) != (n2)) ### NotEqual % 7.05/7.23 6. ((succ (tptp_minus_1)) = (n0)) ((n0) != (succ (tptp_minus_1))) ### Sym(=) % 7.05/7.23 7. (-. (gt (n2) (succ (tptp_minus_1)))) (gt (n2) (n0)) ((succ (tptp_minus_1)) = (n0)) ### Trans 5 6 % 7.05/7.23 8. (-. (gt (succ (n1)) (succ (tptp_minus_1)))) ((succ (succ (n0))) = (n2)) ((succ (tptp_minus_1)) = (n0)) (gt (n2) (n0)) ((succ (n0)) = (n1)) ### TransEq 4 7 7 % 7.05/7.23 9. (T_0 != T_0) ### Refl(=) % 7.05/7.23 10. (-. (gt (succ (n1)) T_0)) (gt (succ (tptp_minus_1)) T_0) ((succ (n0)) = (n1)) (gt (n2) (n0)) ((succ (tptp_minus_1)) = (n0)) ((succ (succ (n0))) = (n2)) ### Trans 8 9 % 7.05/7.23 11. (-. (leq T_0 (n1))) ((succ (succ (n0))) = (n2)) ((succ (tptp_minus_1)) = (n0)) (gt (n2) (n0)) ((succ (n0)) = (n1)) (gt (succ (tptp_minus_1)) T_0) ### Definition-Pseudo(leq) 10 % 7.05/7.23 12. (T_0 != (n0)) (T_0 = (n0)) ### Axiom % 7.05/7.23 13. (T_0 != (n1)) (T_0 = (n1)) ### Axiom % 7.05/7.23 14. (((leq (n0) T_0) /\ (leq T_0 (n1))) => ((T_0 = (n0)) \/ (T_0 = (n1)))) (T_0 != (n1)) (T_0 != (n0)) (gt (succ (tptp_minus_1)) T_0) ((succ (n0)) = (n1)) (gt (n2) (n0)) ((succ (tptp_minus_1)) = (n0)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) ### DisjTree 2 11 12 13 % 7.05/7.23 15. (All X, (((leq (n0) X) /\ (leq X (n1))) => ((X = (n0)) \/ (X = (n1))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (tptp_minus_1)) = (n0)) (gt (n2) (n0)) ((succ (n0)) = (n1)) (gt (succ (tptp_minus_1)) T_0) (T_0 != (n0)) (T_0 != (n1)) ### All 14 % 7.05/7.23 16. ((succ (tptp_minus_1)) = (n0)) ((succ (tptp_minus_1)) != (n0)) ### Axiom % 7.05/7.23 17. ((succ (tptp_minus_1)) != (succ (tptp_minus_1))) ### Refl(=) % 7.05/7.23 18. (-. (gt (succ (tptp_minus_1)) (n0))) (T_0 != (n1)) (gt (succ (tptp_minus_1)) T_0) ((succ (n0)) = (n1)) (gt (n2) (n0)) ((succ (tptp_minus_1)) = (n0)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n1))) => ((X = (n0)) \/ (X = (n1))))) ### Trans 17 15 % 7.05/7.23 19. ((succ (tptp_minus_1)) != (succ (tptp_minus_1))) ### Refl(=) % 7.05/7.23 20. (-. (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))) (All X, (((leq (n0) X) /\ (leq X (n1))) => ((X = (n0)) \/ (X = (n1))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) (gt (n2) (n0)) ((succ (n0)) = (n1)) (gt (succ (tptp_minus_1)) T_0) (T_0 != (n1)) ((succ (tptp_minus_1)) = (n0)) ### TransEq2 16 18 19 % 7.05/7.23 21. ((succ (tptp_minus_1)) != (succ (tptp_minus_1))) ### Refl(=) % 7.05/7.23 22. (-. (gt T_0 (succ (tptp_minus_1)))) (T_0 != (n1)) (gt (succ (tptp_minus_1)) T_0) ((succ (n0)) = (n1)) (gt (n2) (n0)) ((succ (tptp_minus_1)) = (n0)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n1))) => ((X = (n0)) \/ (X = (n1))))) ### TransEq2 15 20 21 % 7.05/7.23 23. ((succ (n0)) != (succ (n0))) ### Refl(=) % 7.05/7.23 24. ((n1) != (n1)) ### NotEqual % 7.05/7.23 25. ((succ (tptp_minus_1)) = (n0)) ((n0) != (succ (tptp_minus_1))) ### Sym(=) % 7.05/7.23 26. (-. (gt (n1) (succ (tptp_minus_1)))) (gt (n1) (n0)) ((succ (tptp_minus_1)) = (n0)) ### Trans 24 25 % 7.05/7.23 27. (-. (gt (succ (n0)) (succ (tptp_minus_1)))) ((succ (n0)) = (n1)) ((succ (tptp_minus_1)) = (n0)) (gt (n1) (n0)) ### TransEq 23 26 26 % 7.05/7.23 28. (gt (n1) (n0)) (All X, (((leq (n0) X) /\ (leq X (n1))) => ((X = (n0)) \/ (X = (n1))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (tptp_minus_1)) = (n0)) (gt (n2) (n0)) ((succ (n0)) = (n1)) (gt (succ (tptp_minus_1)) T_0) (-. (gt T_0 (succ (tptp_minus_1)))) ### TransEq2 22 27 27 % 7.05/7.23 29. (T_0 != T_0) ### Refl(=) % 7.05/7.23 30. (-. (gt T_0 T_0)) (gt (succ (tptp_minus_1)) T_0) ((succ (n0)) = (n1)) (gt (n2) (n0)) ((succ (tptp_minus_1)) = (n0)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n1))) => ((X = (n0)) \/ (X = (n1))))) (gt (n1) (n0)) ### Trans 28 29 % 7.05/7.23 31. (All X, (-. (gt X X))) (gt (n1) (n0)) (All X, (((leq (n0) X) /\ (leq X (n1))) => ((X = (n0)) \/ (X = (n1))))) (gt (succ T_0) (n0)) ((succ (succ (n0))) = (n2)) ((succ (tptp_minus_1)) = (n0)) (gt (n2) (n0)) ((succ (n0)) = (n1)) (gt (succ (tptp_minus_1)) T_0) ### All 30 % 7.05/7.23 32. (leq T_0 (tptp_minus_1)) ((succ (n0)) = (n1)) (gt (n2) (n0)) ((succ (tptp_minus_1)) = (n0)) ((succ (succ (n0))) = (n2)) (gt (succ T_0) (n0)) (All X, (((leq (n0) X) /\ (leq X (n1))) => ((X = (n0)) \/ (X = (n1))))) (gt (n1) (n0)) (All X, (-. (gt X X))) ### Definition-Pseudo(leq) 31 % 7.05/7.23 33. (leq (n0) T_0) (All X, (-. (gt X X))) (gt (n1) (n0)) (All X, (((leq (n0) X) /\ (leq X (n1))) => ((X = (n0)) \/ (X = (n1))))) ((succ (succ (n0))) = (n2)) ((succ (tptp_minus_1)) = (n0)) (gt (n2) (n0)) ((succ (n0)) = (n1)) (leq T_0 (tptp_minus_1)) ### Definition-Pseudo(leq) 32 % 7.05/7.23 34. (-. (((leq (n0) T_0) /\ (leq T_0 (tptp_minus_1))) => ((a_select3 (q) (pv10) T_0) = (divide (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) T_0)) (minus (a_select2 (x) (pv10)) (a_select2 (mu) T_0))) (tptp_minus_2)) (times (a_select2 (sigma) T_0) (a_select2 (sigma) T_0)))) (a_select2 (rho) T_0)) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) T_0))) (sum (n0) (n4) (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index))) (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index)))) (tptp_minus_2)) (times (a_select2 (sigma) (tptp_sum_index)) (a_select2 (sigma) (tptp_sum_index))))) (a_select2 (rho) (tptp_sum_index))) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) (tptp_sum_index))))))))) ((succ (n0)) = (n1)) (gt (n2) (n0)) ((succ (tptp_minus_1)) = (n0)) ((succ (succ (n0))) = (n2)) (All X, (((leq (n0) X) /\ (leq X (n1))) => ((X = (n0)) \/ (X = (n1))))) (gt (n1) (n0)) (All X, (-. (gt X X))) ### ConjTree 33 % 7.05/7.23 35. (-. (All B, (((leq (n0) B) /\ (leq B (tptp_minus_1))) => ((a_select3 (q) (pv10) B) = (divide (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) B)) (minus (a_select2 (x) (pv10)) (a_select2 (mu) B))) (tptp_minus_2)) (times (a_select2 (sigma) B) (a_select2 (sigma) B)))) (a_select2 (rho) B)) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) B))) (sum (n0) (n4) (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index))) (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index)))) (tptp_minus_2)) (times (a_select2 (sigma) (tptp_sum_index)) (a_select2 (sigma) (tptp_sum_index))))) (a_select2 (rho) (tptp_sum_index))) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) (tptp_sum_index)))))))))) (All X, (-. (gt X X))) (gt (n1) (n0)) (All X, (((leq (n0) X) /\ (leq X (n1))) => ((X = (n0)) \/ (X = (n1))))) ((succ (succ (n0))) = (n2)) ((succ (tptp_minus_1)) = (n0)) (gt (n2) (n0)) ((succ (n0)) = (n1)) ### NotAllEx 34 % 7.05/7.23 36. (-. (((leq (n0) (pv10)) /\ ((leq (pv10) (n135299)) /\ (All A, (((leq (n0) A) /\ (leq A (pred (pv10)))) => ((sum (n0) (n4) (a_select3 (q) A (tptp_sum_index))) = (n1)))))) => (All B, (((leq (n0) B) /\ (leq B (tptp_minus_1))) => ((a_select3 (q) (pv10) B) = (divide (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) B)) (minus (a_select2 (x) (pv10)) (a_select2 (mu) B))) (tptp_minus_2)) (times (a_select2 (sigma) B) (a_select2 (sigma) B)))) (a_select2 (rho) B)) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) B))) (sum (n0) (n4) (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index))) (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index)))) (tptp_minus_2)) (times (a_select2 (sigma) (tptp_sum_index)) (a_select2 (sigma) (tptp_sum_index))))) (a_select2 (rho) (tptp_sum_index))) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) (tptp_sum_index))))))))))) ((succ (n0)) = (n1)) (gt (n2) (n0)) ((succ (tptp_minus_1)) = (n0)) ((succ (succ (n0))) = (n2)) (All X, (((leq (n0) X) /\ (leq X (n1))) => ((X = (n0)) \/ (X = (n1))))) (gt (n1) (n0)) (All X, (-. (gt X X))) ### ConjTree 35 % 7.05/7.23 % SZS output end Proof % 7.05/7.23 (* END-PROOF *) %------------------------------------------------------------------------------