%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SWV371+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 : n007.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 21:51:08 EDT 2022 % Result : Theorem 45.10s 45.28s % Output : Proof 45.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SWV371+1 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.34 % Computer : n007.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Tue Jun 14 15:19:55 EDT 2022 % 0.13/0.34 % CPUTime : % 45.10/45.28 % SZS status Theorem % 45.10/45.28 (* PROOF-FOUND *) % 45.10/45.28 (* BEGIN-PROOF *) % 45.10/45.28 % SZS output start Proof % 45.10/45.28 1. (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 % 45.10/45.28 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)))) ### Definition-Pseudo(phi) 1 % 45.10/45.28 3. (-. (contains_pq (i (triple T_0 T_1 T_2)) (findmin_cpq_res (triple T_0 T_1 T_2)))) (contains_pq (i (triple T_0 T_1 T_2)) (findmin_cpq_res (triple T_0 T_1 T_2))) ### Axiom % 45.10/45.28 4. ((phi (findmin_cpq_eff (triple T_0 T_1 T_2))) => (contains_pq (i (triple T_0 T_1 T_2)) (findmin_cpq_res (triple T_0 T_1 T_2)))) (-. (contains_pq (i (triple T_0 T_1 T_2)) (findmin_cpq_res (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)))) ### Imply 2 3 % 45.10/45.28 5. (All W, ((phi (findmin_cpq_eff (triple T_0 T_1 W))) => (contains_pq (i (triple T_0 T_1 W)) (findmin_cpq_res (triple T_0 T_1 W))))) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) (-. (contains_pq (i (triple T_0 T_1 T_2)) (findmin_cpq_res (triple T_0 T_1 T_2)))) ### All 4 % 45.10/45.28 6. (All V, (All W, ((phi (findmin_cpq_eff (triple T_0 V W))) => (contains_pq (i (triple T_0 V W)) (findmin_cpq_res (triple T_0 V W)))))) (-. (contains_pq (i (triple T_0 T_1 T_2)) (findmin_cpq_res (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)))) ### All 5 % 45.10/45.28 7. (All U, (All V, (All W, ((phi (findmin_cpq_eff (triple U V W))) => (contains_pq (i (triple U V W)) (findmin_cpq_res (triple U V W))))))) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) (-. (contains_pq (i (triple T_0 T_1 T_2)) (findmin_cpq_res (triple T_0 T_1 T_2)))) ### All 6 % 45.10/45.28 8. (-. (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 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))) ### Axiom % 45.10/45.28 9. (issmallestelement_pq (i (triple T_0 T_1 T_2)) (findmin_cpq_res (triple T_0 T_1 T_2))) (-. (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)))) ### Definition-Pseudo(issmallestelement_pq) 8 % 45.10/45.28 10. ((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 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)))) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) ### Imply 2 9 % 45.10/45.28 11. (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))))) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) (-. (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 10 % 45.10/45.28 12. (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 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)))) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) ### All 11 % 45.10/45.28 13. (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))))))) (Ex V, ((succ_cpq (findmin_cpq_eff (triple T_0 T_1 T_2)) V) /\ ((ok V) /\ (check_cpq V)))) (-. (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 12 % 45.10/45.28 14. (-. (issmallestelement_pq (i (triple T_0 T_1 T_2)) (findmin_cpq_res (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)))) (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))))))) ### Definition-Pseudo(issmallestelement_pq) 13 % 45.10/45.28 15. (-. ((contains_pq (i (triple T_0 T_1 T_2)) (findmin_cpq_res (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, ((phi (findmin_cpq_eff (triple U V W))) => (issmallestelement_pq (i (triple U V W)) (findmin_cpq_res (triple U V W))))))) (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, ((phi (findmin_cpq_eff (triple U V W))) => (contains_pq (i (triple U V W)) (findmin_cpq_res (triple U V W))))))) ### NotAnd 7 14 % 45.10/45.28 16. (-. (pi_sharp_find_min (i (triple T_0 T_1 T_2)) (findmin_cpq_res (triple T_0 T_1 T_2)))) (All U, (All V, (All W, ((phi (findmin_cpq_eff (triple U V W))) => (contains_pq (i (triple U V W)) (findmin_cpq_res (triple U V W))))))) (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, ((phi (findmin_cpq_eff (triple U V W))) => (issmallestelement_pq (i (triple U V W)) (findmin_cpq_res (triple U V W))))))) ### Definition-Pseudo(pi_sharp_find_min) 15 % 45.10/45.28 17. (phi (findmin_cpq_eff (triple T_0 T_1 T_2))) (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, (All W, ((phi (findmin_cpq_eff (triple U V W))) => (contains_pq (i (triple U V W)) (findmin_cpq_res (triple U V W))))))) (-. (pi_sharp_find_min (i (triple T_0 T_1 T_2)) (findmin_cpq_res (triple T_0 T_1 T_2)))) ### Definition-Pseudo(phi) 16 % 45.10/45.28 18. (-. ((phi (findmin_cpq_eff (triple T_0 T_1 T_2))) => (pi_sharp_find_min (i (triple T_0 T_1 T_2)) (findmin_cpq_res (triple T_0 T_1 T_2))))) (All U, (All V, (All W, ((phi (findmin_cpq_eff (triple U V W))) => (contains_pq (i (triple U V W)) (findmin_cpq_res (triple U V W))))))) (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))))))) ### NotImply 17 % 45.10/45.28 19. (-. (All W, ((phi (findmin_cpq_eff (triple T_0 T_1 W))) => (pi_sharp_find_min (i (triple T_0 T_1 W)) (findmin_cpq_res (triple T_0 T_1 W)))))) (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, (All W, ((phi (findmin_cpq_eff (triple U V W))) => (contains_pq (i (triple U V W)) (findmin_cpq_res (triple U V W))))))) ### NotAllEx 18 % 45.10/45.28 20. (-. (All V, (All W, ((phi (findmin_cpq_eff (triple T_0 V W))) => (pi_sharp_find_min (i (triple T_0 V W)) (findmin_cpq_res (triple T_0 V W))))))) (All U, (All V, (All W, ((phi (findmin_cpq_eff (triple U V W))) => (contains_pq (i (triple U V W)) (findmin_cpq_res (triple U V W))))))) (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))))))) ### NotAllEx 19 % 45.10/45.28 21. (-. (All U, (All V, (All W, ((phi (findmin_cpq_eff (triple U V W))) => (pi_sharp_find_min (i (triple U V W)) (findmin_cpq_res (triple U V W)))))))) (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, (All W, ((phi (findmin_cpq_eff (triple U V W))) => (contains_pq (i (triple U V W)) (findmin_cpq_res (triple U V W))))))) ### NotAllEx 20 % 45.10/45.28 % SZS output end Proof % 45.10/45.28 (* END-PROOF *) %------------------------------------------------------------------------------