%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SWV153+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 : 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 21:50:10 EDT 2022 % Result : Theorem 127.32s 127.57s % Output : Proof 127.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.08 % Problem : SWV153+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.02/0.09 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.08/0.28 % Computer : n025.cluster.edu % 0.08/0.28 % Model : x86_64 x86_64 % 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.28 % Memory : 8042.1875MB % 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.29 % CPULimit : 300 % 0.08/0.29 % WCLimit : 600 % 0.08/0.29 % DateTime : Wed Jun 15 04:59:10 EDT 2022 % 0.08/0.29 % CPUTime : % 127.32/127.57 % SZS status Theorem % 127.32/127.57 (* PROOF-FOUND *) % 127.32/127.57 (* BEGIN-PROOF *) % 127.32/127.57 % SZS output start Proof % 127.32/127.57 1. (gt (succ T_0) (n0)) (-. (gt (succ T_0) (n0))) ### Axiom % 127.32/127.57 2. (-. (leq (n0) T_0)) (gt (succ T_0) (n0)) ### Definition-Pseudo(leq) 1 % 127.32/127.57 3. (gt (succ (pv12)) T_0) (-. (gt (succ (pv12)) T_0)) ### Axiom % 127.32/127.57 4. (-. (leq T_0 (pv12))) (gt (succ (pv12)) T_0) ### Definition-Pseudo(leq) 3 % 127.32/127.57 5. ((pv12) != T_0) (T_0 = (pv12)) ### Sym(=) % 127.32/127.57 6. (-. (gt (pv12) T_0)) (gt (pv12) T_0) ### Axiom % 127.32/127.57 7. (((leq T_0 (pv12)) /\ (T_0 != (pv12))) => (gt (pv12) T_0)) (-. (gt (pv12) T_0)) ((pv12) != T_0) (gt (succ (pv12)) T_0) ### DisjTree 4 5 6 % 127.32/127.57 8. (All Y, (((leq T_0 Y) /\ (T_0 != Y)) => (gt Y T_0))) (gt (succ (pv12)) T_0) ((pv12) != T_0) (-. (gt (pv12) T_0)) ### All 7 % 127.32/127.57 9. (All X, (All Y, (((leq X Y) /\ (X != Y)) => (gt Y X)))) (-. (gt (pv12) T_0)) ((pv12) != T_0) (gt (succ (pv12)) T_0) ### All 8 % 127.32/127.57 10. (-. (gt (succ (pred (pv12))) T_0)) (gt (succ (pred (pv12))) T_0) ### Axiom % 127.32/127.57 11. (leq T_0 (pred (pv12))) (-. (gt (succ (pred (pv12))) T_0)) ### Definition-Pseudo(leq) 10 % 127.32/127.57 12. ((leq T_0 (pred (pv12))) <=> (gt (pv12) T_0)) (-. (gt (succ (pred (pv12))) T_0)) (gt (succ (pv12)) T_0) ((pv12) != T_0) (All X, (All Y, (((leq X Y) /\ (X != Y)) => (gt Y X)))) ### Equiv 9 11 % 127.32/127.57 13. (All Y, ((leq T_0 (pred Y)) <=> (gt Y T_0))) (All X, (All Y, (((leq X Y) /\ (X != Y)) => (gt Y X)))) ((pv12) != T_0) (gt (succ (pv12)) T_0) (-. (gt (succ (pred (pv12))) T_0)) ### All 12 % 127.32/127.57 14. (-. (leq T_0 (pred (pv12)))) (gt (succ (pv12)) T_0) ((pv12) != T_0) (All X, (All Y, (((leq X Y) /\ (X != Y)) => (gt Y X)))) (All Y, ((leq T_0 (pred Y)) <=> (gt Y T_0))) ### Definition-Pseudo(leq) 13 % 127.32/127.57 15. ((a_select3 (q) (pv10) T_0) != (divide (sqrt (times (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))) ((a_select3 (q) (pv10) T_0) = (divide (sqrt (times (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))) ### Axiom % 127.32/127.57 16. (((leq (n0) T_0) /\ (leq T_0 (pred (pv12)))) => ((a_select3 (q) (pv10) T_0) = (divide (sqrt (times (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))))))))) ((a_select3 (q) (pv10) T_0) != (divide (sqrt (times (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))) (All Y, ((leq T_0 (pred Y)) <=> (gt Y T_0))) (All X, (All Y, (((leq X Y) /\ (X != Y)) => (gt Y X)))) ((pv12) != T_0) (gt (succ (pv12)) T_0) (gt (succ T_0) (n0)) ### DisjTree 2 14 15 % 127.32/127.57 17. (All A, (((leq (n0) A) /\ (leq A (pred (pv12)))) => ((a_select3 (q) (pv10) A) = (divide (sqrt (times (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))))) (gt (succ T_0) (n0)) (gt (succ (pv12)) T_0) ((pv12) != T_0) (All X, (All Y, (((leq X Y) /\ (X != Y)) => (gt Y X)))) (All Y, ((leq T_0 (pred Y)) <=> (gt Y T_0))) ((a_select3 (q) (pv10) T_0) != (divide (sqrt (times (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))) ### All 16 % 127.32/127.57 18. (All X, (All Y, ((leq X (pred Y)) <=> (gt Y X)))) ((a_select3 (q) (pv10) T_0) != (divide (sqrt (times (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))) (All X, (All Y, (((leq X Y) /\ (X != Y)) => (gt Y X)))) ((pv12) != T_0) (gt (succ (pv12)) T_0) (gt (succ T_0) (n0)) (All A, (((leq (n0) A) /\ (leq A (pred (pv12)))) => ((a_select3 (q) (pv10) A) = (divide (sqrt (times (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))))) ### All 17 % 127.32/127.57 19. (leq T_0 (pv12)) (All A, (((leq (n0) A) /\ (leq A (pred (pv12)))) => ((a_select3 (q) (pv10) A) = (divide (sqrt (times (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))))) (gt (succ T_0) (n0)) ((pv12) != T_0) (All X, (All Y, (((leq X Y) /\ (X != Y)) => (gt Y X)))) ((a_select3 (q) (pv10) T_0) != (divide (sqrt (times (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))) (All X, (All Y, ((leq X (pred Y)) <=> (gt Y X)))) ### Definition-Pseudo(leq) 18 % 127.32/127.57 20. (leq (n0) T_0) (All X, (All Y, ((leq X (pred Y)) <=> (gt Y X)))) ((a_select3 (q) (pv10) T_0) != (divide (sqrt (times (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))) (All X, (All Y, (((leq X Y) /\ (X != Y)) => (gt Y X)))) ((pv12) != T_0) (All A, (((leq (n0) A) /\ (leq A (pred (pv12)))) => ((a_select3 (q) (pv10) A) = (divide (sqrt (times (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))))) (leq T_0 (pv12)) ### Definition-Pseudo(leq) 19 % 127.32/127.57 21. (-. (((leq (n0) T_0) /\ (leq T_0 (pv12))) => (((pv12) != T_0) => ((a_select3 (q) (pv10) T_0) = (divide (sqrt (times (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) T_0 (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))))))))))) (All A, (((leq (n0) A) /\ (leq A (pred (pv12)))) => ((a_select3 (q) (pv10) A) = (divide (sqrt (times (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))))) (All X, (All Y, (((leq X Y) /\ (X != Y)) => (gt Y X)))) (All X, (All Y, ((leq X (pred Y)) <=> (gt Y X)))) ### ConjTree 20 % 127.32/127.57 22. (-. (All C, (((leq (n0) C) /\ (leq C (pv12))) => (((pv12) != C) => ((a_select3 (q) (pv10) C) = (divide (sqrt (times (minus (a_select3 (center) C (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) C (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))))))) (All X, (All Y, ((leq X (pred Y)) <=> (gt Y X)))) (All X, (All Y, (((leq X Y) /\ (X != Y)) => (gt Y X)))) (All A, (((leq (n0) A) /\ (leq A (pred (pv12)))) => ((a_select3 (q) (pv10) A) = (divide (sqrt (times (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))))) ### NotAllEx 21 % 127.32/127.58 23. (-. ((((pv70) = (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))))))) /\ ((leq (n0) (pv10)) /\ ((leq (n0) (pv12)) /\ ((leq (pv10) (n135299)) /\ ((leq (pv12) (n4)) /\ ((All A, (((leq (n0) A) /\ (leq A (pred (pv12)))) => ((a_select3 (q) (pv10) A) = (divide (sqrt (times (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) A (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10)))))))))) /\ (All B, (((leq (n0) B) /\ (leq B (pred (pv10)))) => ((sum (n0) (n4) (a_select3 (q) B (tptp_sum_index))) = (n1)))))))))) => (All C, (((leq (n0) C) /\ (leq C (pv12))) => (((pv12) != C) => ((a_select3 (q) (pv10) C) = (divide (sqrt (times (minus (a_select3 (center) C (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) C (n0)) (a_select2 (x) (pv10))))) (sum (n0) (n4) (sqrt (times (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))) (minus (a_select3 (center) (tptp_sum_index) (n0)) (a_select2 (x) (pv10))))))))))))) (All X, (All Y, (((leq X Y) /\ (X != Y)) => (gt Y X)))) (All X, (All Y, ((leq X (pred Y)) <=> (gt Y X)))) ### ConjTree 22 % 127.32/127.58 % SZS output end Proof % 127.32/127.58 (* END-PROOF *) %------------------------------------------------------------------------------