TSTP Solution File: NUM427+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : NUM427+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n024.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 : Mon Jul 18 14:42:21 EDT 2022
% Result : Theorem 242.06s 242.26s
% Output : Proof 242.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM427+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 13:32:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 242.06/242.26 % SZS status Theorem
% 242.06/242.26 (* PROOF-FOUND *)
% 242.06/242.26 (* BEGIN-PROOF *)
% 242.06/242.26 % SZS output start Proof
% 242.06/242.26 1. (aInteger0 (xb)) (-. (aInteger0 (xb))) ### Axiom
% 242.06/242.26 2. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom
% 242.06/242.26 3. (aInteger0 (xq)) (-. (aInteger0 (xq))) ### Axiom
% 242.06/242.26 4. ((xq) != (sz00)) ((xq) = (sz00)) ### Axiom
% 242.06/242.26 5. (aInteger0 (xb)) (-. (aInteger0 (xb))) ### Axiom
% 242.06/242.26 6. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom
% 242.06/242.26 7. (-. (aInteger0 (smndt0 (xa)))) (aInteger0 (smndt0 (xa))) ### Axiom
% 242.06/242.26 8. ((aInteger0 (xa)) => (aInteger0 (smndt0 (xa)))) (-. (aInteger0 (smndt0 (xa)))) (aInteger0 (xa)) ### Imply 6 7
% 242.06/242.26 9. (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) (-. (aInteger0 (smndt0 (xa)))) ### All 8
% 242.06/242.26 10. (-. (aInteger0 (sdtpldt0 (xb) (smndt0 (xa))))) (aInteger0 (sdtpldt0 (xb) (smndt0 (xa)))) ### Axiom
% 242.06/242.26 11. (((aInteger0 (xb)) /\ (aInteger0 (smndt0 (xa)))) => (aInteger0 (sdtpldt0 (xb) (smndt0 (xa))))) (-. (aInteger0 (sdtpldt0 (xb) (smndt0 (xa))))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xb)) ### DisjTree 5 9 10
% 242.06/242.26 12. (All W1, (((aInteger0 (xb)) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 (xb) W1)))) (aInteger0 (xb)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) (-. (aInteger0 (sdtpldt0 (xb) (smndt0 (xa))))) ### All 11
% 242.06/242.26 13. (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (-. (aInteger0 (sdtpldt0 (xb) (smndt0 (xa))))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xb)) ### All 12
% 242.06/242.26 14. (aInteger0 (xq)) (-. (aInteger0 (xq))) ### Axiom
% 242.06/242.26 15. ((xq) != (sz00)) ((xq) = (sz00)) ### Axiom
% 242.06/242.26 16. (aInteger0 (xn)) (-. (aInteger0 (xn))) ### Axiom
% 242.06/242.26 17. (-. (aInteger0 (smndt0 (xn)))) (aInteger0 (smndt0 (xn))) ### Axiom
% 242.06/242.26 18. ((aInteger0 (xn)) => (aInteger0 (smndt0 (xn)))) (-. (aInteger0 (smndt0 (xn)))) (aInteger0 (xn)) ### Imply 16 17
% 242.06/242.26 19. (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xn)) (-. (aInteger0 (smndt0 (xn)))) ### All 18
% 242.06/242.26 20. ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) ((sdtasdt0 (xq) (smndt0 (xn))) != (sdtpldt0 (xb) (smndt0 (xa)))) ### Axiom
% 242.06/242.26 21. (-. ((aInteger0 (smndt0 (xn))) /\ ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))))) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) (aInteger0 (xn)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) ### NotAnd 19 20
% 242.06/242.26 22. (-. (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 (xq) W2) = (sdtpldt0 (xb) (smndt0 (xa))))))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xn)) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) ### NotExists 21
% 242.06/242.26 23. (-. ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 (xq) W2) = (sdtpldt0 (xb) (smndt0 (xa))))))))) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) (aInteger0 (xn)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) ((xq) != (sz00)) (aInteger0 (xq)) ### DisjTree 14 15 22
% 242.06/242.26 24. (-. (aDivisorOf0 (xq) (sdtpldt0 (xb) (smndt0 (xa))))) (aDivisorOf0 (xq) (sdtpldt0 (xb) (smndt0 (xa)))) ### Axiom
% 242.06/242.26 25. ((aDivisorOf0 (xq) (sdtpldt0 (xb) (smndt0 (xa)))) <=> ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 (xq) W2) = (sdtpldt0 (xb) (smndt0 (xa))))))))) (-. (aDivisorOf0 (xq) (sdtpldt0 (xb) (smndt0 (xa))))) (aInteger0 (xq)) ((xq) != (sz00)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xn)) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) ### Equiv 23 24
% 242.06/242.26 26. (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xb) (smndt0 (xa)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xb) (smndt0 (xa)))))))))) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) (aInteger0 (xn)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) ((xq) != (sz00)) (aInteger0 (xq)) (-. (aDivisorOf0 (xq) (sdtpldt0 (xb) (smndt0 (xa))))) ### All 25
% 242.06/242.26 27. ((aInteger0 (sdtpldt0 (xb) (smndt0 (xa)))) => (All W1, ((aDivisorOf0 W1 (sdtpldt0 (xb) (smndt0 (xa)))) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = (sdtpldt0 (xb) (smndt0 (xa))))))))))) (-. (aDivisorOf0 (xq) (sdtpldt0 (xb) (smndt0 (xa))))) (aInteger0 (xq)) ((xq) != (sz00)) (aInteger0 (xn)) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) (aInteger0 (xb)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) ### Imply 13 26
% 242.06/242.26 28. (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (aInteger0 (xa)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xb)) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) (aInteger0 (xn)) ((xq) != (sz00)) (aInteger0 (xq)) (-. (aDivisorOf0 (xq) (sdtpldt0 (xb) (smndt0 (xa))))) ### All 27
% 242.06/242.26 29. (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq)) ### Axiom
% 242.06/242.26 30. ((sdteqdtlpzmzozddtrp0 (xb) (xa) (xq)) <=> (aDivisorOf0 (xq) (sdtpldt0 (xb) (smndt0 (xa))))) (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) (aInteger0 (xq)) ((xq) != (sz00)) (aInteger0 (xn)) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) (aInteger0 (xb)) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (aInteger0 (xa)) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) ### Equiv 28 29
% 242.06/242.26 31. (((aInteger0 (xb)) /\ ((aInteger0 (xa)) /\ ((aInteger0 (xq)) /\ ((xq) != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xb) (xa) (xq)) <=> (aDivisorOf0 (xq) (sdtpldt0 (xb) (smndt0 (xa)))))) (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) (aInteger0 (xn)) (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xa)) (aInteger0 (xb)) ### DisjTree 1 2 3 4 30
% 242.06/242.26 32. (All W2, (((aInteger0 (xb)) /\ ((aInteger0 (xa)) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xb) (xa) W2) <=> (aDivisorOf0 W2 (sdtpldt0 (xb) (smndt0 (xa))))))) (aInteger0 (xb)) (aInteger0 (xa)) (aInteger0 (xq)) ((xq) != (sz00)) (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) (aInteger0 (xn)) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) ### All 31
% 242.06/242.26 33. (All W1, (All W2, (((aInteger0 (xb)) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xb) W1 W2) <=> (aDivisorOf0 W2 (sdtpldt0 (xb) (smndt0 W1))))))) (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) (aInteger0 (xn)) (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xa)) (aInteger0 (xb)) ### All 32
% 242.06/242.26 34. (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) <=> (aDivisorOf0 W2 (sdtpldt0 W0 (smndt0 W1)))))))) (aInteger0 (xb)) (aInteger0 (xa)) (aInteger0 (xq)) ((xq) != (sz00)) (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) (aInteger0 (xn)) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) ### All 33
% 242.06/242.26 35. ((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 (xq)) /\ ((xq) != (sz00))))) (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) (aInteger0 (xn)) (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) <=> (aDivisorOf0 W2 (sdtpldt0 W0 (smndt0 W1)))))))) ### ConjTree 34
% 242.06/242.26 36. ((aInteger0 (xn)) /\ ((sdtasdt0 (xq) (xn)) = (sdtpldt0 (xa) (smndt0 (xb))))) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) <=> (aDivisorOf0 W2 (sdtpldt0 W0 (smndt0 W1)))))))) (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) ((sdtasdt0 (xq) (smndt0 (xn))) = (sdtpldt0 (xb) (smndt0 (xa)))) (All W0, ((aInteger0 W0) => (aInteger0 (smndt0 W0)))) (All W0, (All W1, (((aInteger0 W0) /\ (aInteger0 W1)) => (aInteger0 (sdtpldt0 W0 W1))))) (All W0, ((aInteger0 W0) => (All W1, ((aDivisorOf0 W1 W0) <=> ((aInteger0 W1) /\ ((W1 != (sz00)) /\ (Ex W2, ((aInteger0 W2) /\ ((sdtasdt0 W1 W2) = W0))))))))) ((aInteger0 (xa)) /\ ((aInteger0 (xb)) /\ ((aInteger0 (xq)) /\ ((xq) != (sz00))))) ### And 35
% 242.06/242.26 % SZS output end Proof
% 242.06/242.26 (* END-PROOF *)
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