%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SWV381+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n025.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 21:51:10 EDT 2022 % Result : Theorem 50.45s 50.64s % Output : Proof 50.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SWV381+1 : TPTP v8.1.0. Released v3.3.0. % 0.10/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.33 % Computer : n025.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 : Tue Jun 14 19:03:10 EDT 2022 % 0.13/0.33 % CPUTime : % 50.45/50.64 % SZS status Theorem % 50.45/50.64 (* PROOF-FOUND *) % 50.45/50.64 (* BEGIN-PROOF *) % 50.45/50.64 % SZS output start Proof % 50.45/50.64 1. (contains_pq (i (triple T_0 T_1 T_2)) T_3) (-. (contains_pq (i (triple T_0 T_1 T_2)) T_3)) ### Axiom % 50.45/50.64 2. (-. (contains_cpq (triple T_0 T_1 T_2) T_3)) (contains_cpq (triple T_0 T_1 T_2) T_3) ### Axiom % 50.45/50.64 3. ((contains_cpq (triple T_0 T_1 T_2) T_3) <=> (contains_pq (i (triple T_0 T_1 T_2)) T_3)) (-. (contains_cpq (triple T_0 T_1 T_2) T_3)) (contains_pq (i (triple T_0 T_1 T_2)) T_3) ### Equiv 1 2 % 50.45/50.64 4. (All X, ((contains_cpq (triple T_0 T_1 T_2) X) <=> (contains_pq (i (triple T_0 T_1 T_2)) X))) (contains_pq (i (triple T_0 T_1 T_2)) T_3) (-. (contains_cpq (triple T_0 T_1 T_2) T_3)) ### All 3 % 50.45/50.64 5. (All W, (All X, ((contains_cpq (triple T_0 T_1 W) X) <=> (contains_pq (i (triple T_0 T_1 W)) X)))) (-. (contains_cpq (triple T_0 T_1 T_2) T_3)) (contains_pq (i (triple T_0 T_1 T_2)) T_3) ### All 4 % 50.45/50.64 6. (All V, (All W, (All X, ((contains_cpq (triple T_0 V W) X) <=> (contains_pq (i (triple T_0 V W)) X))))) (contains_pq (i (triple T_0 T_1 T_2)) T_3) (-. (contains_cpq (triple T_0 T_1 T_2) T_3)) ### All 5 % 50.45/50.64 7. (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) (-. (contains_cpq (triple T_0 T_1 T_2) T_3)) (contains_pq (i (triple T_0 T_1 T_2)) T_3) ### All 6 % 50.45/50.64 8. (-. (less_than T_3 (findmin_cpq_res (triple T_0 T_1 T_2)))) (less_than T_3 (findmin_cpq_res (triple T_0 T_1 T_2))) ### Axiom % 50.45/50.64 9. (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3) ### Axiom % 50.45/50.64 10. ((less_than T_3 (findmin_cpq_res (triple T_0 T_1 T_2))) \/ (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) (-. (less_than T_3 (findmin_cpq_res (triple T_0 T_1 T_2)))) ### Or 8 9 % 50.45/50.64 11. (All V, ((less_than T_3 V) \/ (less_than V T_3))) (-. (less_than T_3 (findmin_cpq_res (triple T_0 T_1 T_2)))) (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) ### All 10 % 50.45/50.64 12. (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3) ### Axiom % 50.45/50.64 13. (-. (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3))) (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) ### NotNot 12 % 50.45/50.64 14. (-. ((less_than T_3 (findmin_cpq_res (triple T_0 T_1 T_2))) /\ (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)))) (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) (All V, ((less_than T_3 V) \/ (less_than V T_3))) ### NotAnd 11 13 % 50.45/50.64 15. (-. (strictly_less_than T_3 (findmin_cpq_res (triple T_0 T_1 T_2)))) (All V, ((less_than T_3 V) \/ (less_than V T_3))) (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) ### Definition-Pseudo(strictly_less_than) 14 % 50.45/50.64 16. (-. ((contains_cpq (triple T_0 T_1 T_2) T_3) /\ (strictly_less_than T_3 (findmin_cpq_res (triple T_0 T_1 T_2))))) (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) (All V, ((less_than T_3 V) \/ (less_than V T_3))) (contains_pq (i (triple T_0 T_1 T_2)) T_3) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) ### NotAnd 7 15 % 50.45/50.64 17. (-. (Ex X, ((contains_cpq (triple T_0 T_1 T_2) X) /\ (strictly_less_than X (findmin_cpq_res (triple T_0 T_1 T_2)))))) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) (contains_pq (i (triple T_0 T_1 T_2)) T_3) (All V, ((less_than T_3 V) \/ (less_than V T_3))) (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) ### NotExists 16 % 50.45/50.64 18. (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) (-. (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V))))) ### Axiom % 50.45/50.64 19. (-. (phi (findmin_cpq_eff (triple T_0 T_1 T_2)))) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) ### Definition-Pseudo(phi) 18 % 50.45/50.64 20. ((Ex X, ((contains_cpq (triple T_0 T_1 T_2) X) /\ (strictly_less_than X (findmin_cpq_res (triple T_0 T_1 T_2))))) => (-. (phi (findmin_cpq_eff (triple T_0 T_1 T_2))))) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) (All V, ((less_than T_3 V) \/ (less_than V T_3))) (contains_pq (i (triple T_0 T_1 T_2)) T_3) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) ### Imply 17 19 % 50.45/50.64 21. (All W, ((Ex X, ((contains_cpq (triple T_0 T_1 W) X) /\ (strictly_less_than X (findmin_cpq_res (triple T_0 T_1 W))))) => (-. (phi (findmin_cpq_eff (triple T_0 T_1 W)))))) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) (contains_pq (i (triple T_0 T_1 T_2)) T_3) (All V, ((less_than T_3 V) \/ (less_than V T_3))) (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) ### All 20 % 50.45/50.64 22. (All V, (All W, ((Ex X, ((contains_cpq (triple T_0 V W) X) /\ (strictly_less_than X (findmin_cpq_res (triple T_0 V W))))) => (-. (phi (findmin_cpq_eff (triple T_0 V W))))))) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) (All V, ((less_than T_3 V) \/ (less_than V T_3))) (contains_pq (i (triple T_0 T_1 T_2)) T_3) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) ### All 21 % 50.45/50.64 23. (All U, (All V, (All W, ((Ex X, ((contains_cpq (triple U V W) X) /\ (strictly_less_than X (findmin_cpq_res (triple U V W))))) => (-. (phi (findmin_cpq_eff (triple U V W)))))))) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) (contains_pq (i (triple T_0 T_1 T_2)) T_3) (All V, ((less_than T_3 V) \/ (less_than V T_3))) (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) ### All 22 % 50.45/50.64 24. (All U, (All V, ((less_than U V) \/ (less_than V U)))) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) (-. (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3)) (contains_pq (i (triple T_0 T_1 T_2)) T_3) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) (All U, (All V, (All W, ((Ex X, ((contains_cpq (triple U V W) X) /\ (strictly_less_than X (findmin_cpq_res (triple U V W))))) => (-. (phi (findmin_cpq_eff (triple U V W)))))))) ### All 23 % 50.45/50.64 25. (-. ((contains_pq (i (triple T_0 T_1 T_2)) T_3) => (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) T_3))) (All U, (All V, (All W, ((Ex X, ((contains_cpq (triple U V W) X) /\ (strictly_less_than X (findmin_cpq_res (triple U V W))))) => (-. (phi (findmin_cpq_eff (triple U V W)))))))) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) (All U, (All V, ((less_than U V) \/ (less_than V U)))) ### NotImply 24 % 50.45/50.64 26. (-. (All W, ((contains_pq (i (triple T_0 T_1 T_2)) W) => (less_than (findmin_cpq_res (triple T_0 T_1 T_2)) W)))) (All U, (All V, ((less_than U V) \/ (less_than V U)))) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) (All U, (All V, (All W, ((Ex X, ((contains_cpq (triple U V W) X) /\ (strictly_less_than X (findmin_cpq_res (triple U V W))))) => (-. (phi (findmin_cpq_eff (triple U V W)))))))) ### NotAllEx 25 % 50.45/50.64 27. (-. (issmallestelement_pq (i (triple T_0 T_1 T_2)) (findmin_cpq_res (triple T_0 T_1 T_2)))) (All U, (All V, (All W, ((Ex X, ((contains_cpq (triple U V W) X) /\ (strictly_less_than X (findmin_cpq_res (triple U V W))))) => (-. (phi (findmin_cpq_eff (triple U V W)))))))) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) (All U, (All V, ((less_than U V) \/ (less_than V U)))) ### Definition-Pseudo(issmallestelement_pq) 26 % 50.45/50.64 28. (phi (findmin_cpq_eff (triple T_0 T_1 T_2))) (All U, (All V, ((less_than U V) \/ (less_than V U)))) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) (All U, (All V, (All W, ((Ex X, ((contains_cpq (triple U V W) X) /\ (strictly_less_than X (findmin_cpq_res (triple U V W))))) => (-. (phi (findmin_cpq_eff (triple U V W)))))))) (-. (issmallestelement_pq (i (triple T_0 T_1 T_2)) (findmin_cpq_res (triple T_0 T_1 T_2)))) ### Definition-Pseudo(phi) 27 % 50.45/50.64 29. (-. ((phi (findmin_cpq_eff (triple T_0 T_1 T_2))) => (issmallestelement_pq (i (triple T_0 T_1 T_2)) (findmin_cpq_res (triple T_0 T_1 T_2))))) (All U, (All V, (All W, ((Ex X, ((contains_cpq (triple U V W) X) /\ (strictly_less_than X (findmin_cpq_res (triple U V W))))) => (-. (phi (findmin_cpq_eff (triple U V W)))))))) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) (All U, (All V, ((less_than U V) \/ (less_than V U)))) ### NotImply 28 % 50.45/50.64 30. (-. (All W, ((phi (findmin_cpq_eff (triple T_0 T_1 W))) => (issmallestelement_pq (i (triple T_0 T_1 W)) (findmin_cpq_res (triple T_0 T_1 W)))))) (All U, (All V, ((less_than U V) \/ (less_than V U)))) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) (All U, (All V, (All W, ((Ex X, ((contains_cpq (triple U V W) X) /\ (strictly_less_than X (findmin_cpq_res (triple U V W))))) => (-. (phi (findmin_cpq_eff (triple U V W)))))))) ### NotAllEx 29 % 50.45/50.64 31. (-. (All V, (All W, ((phi (findmin_cpq_eff (triple T_0 V W))) => (issmallestelement_pq (i (triple T_0 V W)) (findmin_cpq_res (triple T_0 V W))))))) (All U, (All V, (All W, ((Ex X, ((contains_cpq (triple U V W) X) /\ (strictly_less_than X (findmin_cpq_res (triple U V W))))) => (-. (phi (findmin_cpq_eff (triple U V W)))))))) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) (All U, (All V, ((less_than U V) \/ (less_than V U)))) ### NotAllEx 30 % 50.45/50.64 32. (-. (All U, (All V, (All W, ((phi (findmin_cpq_eff (triple U V W))) => (issmallestelement_pq (i (triple U V W)) (findmin_cpq_res (triple U V W)))))))) (All U, (All V, ((less_than U V) \/ (less_than V U)))) (All U, (All V, (All W, (All X, ((contains_cpq (triple U V W) X) <=> (contains_pq (i (triple U V W)) X)))))) (All U, (All V, (All W, ((Ex X, ((contains_cpq (triple U V W) X) /\ (strictly_less_than X (findmin_cpq_res (triple U V W))))) => (-. (phi (findmin_cpq_eff (triple U V W)))))))) ### NotAllEx 31 % 50.45/50.64 % SZS output end Proof % 50.45/50.64 (* END-PROOF *) %------------------------------------------------------------------------------