TSTP Solution File: SWV381+1 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% 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 *)
%------------------------------------------------------------------------------