TSTP Solution File: NUM443+4 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : NUM443+4 : 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 : n003.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 14:42:30 EDT 2022
% Result : Theorem 1.16s 1.34s
% Output : Proof 1.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM443+4 : 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 : n003.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 : Fri Jul 8 02:25:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.16/1.34 % SZS status Theorem
% 1.16/1.34 (* PROOF-FOUND *)
% 1.16/1.34 (* BEGIN-PROOF *)
% 1.16/1.34 % SZS output start Proof
% 1.16/1.34 1. (aInteger0 (xb)) (-. (aInteger0 (xb))) ### Axiom
% 1.16/1.34 2. (aInteger0 (xb)) (-. (aInteger0 (xb))) ### Axiom
% 1.16/1.34 3. (aInteger0 (xc)) (-. (aInteger0 (xc))) ### Axiom
% 1.16/1.34 4. (aInteger0 (xq)) (-. (aInteger0 (xq))) ### Axiom
% 1.16/1.34 5. ((xq) != (sz00)) ((xq) = (sz00)) ### Axiom
% 1.16/1.34 6. (aInteger0 (xa)) (-. (aInteger0 (xa))) ### Axiom
% 1.16/1.34 7. (aInteger0 (xc)) (-. (aInteger0 (xc))) ### Axiom
% 1.16/1.34 8. (aInteger0 (xb)) (-. (aInteger0 (xb))) ### Axiom
% 1.16/1.34 9. (aInteger0 (xq)) (-. (aInteger0 (xq))) ### Axiom
% 1.16/1.34 10. ((xq) != (sz00)) ((xq) = (sz00)) ### Axiom
% 1.16/1.34 11. (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) (-. (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq))) ### Axiom
% 1.16/1.34 12. (-. (sdteqdtlpzmzozddtrp0 (xb) (xc) (xq))) (sdteqdtlpzmzozddtrp0 (xb) (xc) (xq)) ### Axiom
% 1.16/1.34 13. (((aInteger0 (xc)) /\ ((aInteger0 (xb)) /\ ((aInteger0 (xq)) /\ ((xq) != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) => (sdteqdtlpzmzozddtrp0 (xb) (xc) (xq)))) (-. (sdteqdtlpzmzozddtrp0 (xb) (xc) (xq))) (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xb)) (aInteger0 (xc)) ### DisjTree 7 8 9 10 11 12
% 1.16/1.34 14. (All W2, (((aInteger0 (xc)) /\ ((aInteger0 (xb)) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xc) (xb) W2) => (sdteqdtlpzmzozddtrp0 (xb) (xc) W2)))) (aInteger0 (xc)) (aInteger0 (xb)) (aInteger0 (xq)) ((xq) != (sz00)) (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) (-. (sdteqdtlpzmzozddtrp0 (xb) (xc) (xq))) ### All 13
% 1.16/1.34 15. (All W1, (All W2, (((aInteger0 (xc)) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 (xc) W1 W2) => (sdteqdtlpzmzozddtrp0 W1 (xc) W2))))) (-. (sdteqdtlpzmzozddtrp0 (xb) (xc) (xq))) (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xb)) (aInteger0 (xc)) ### All 14
% 1.16/1.34 16. (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) => (sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (aInteger0 (xc)) (aInteger0 (xb)) (aInteger0 (xq)) ((xq) != (sz00)) (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) (-. (sdteqdtlpzmzozddtrp0 (xb) (xc) (xq))) ### All 15
% 1.16/1.34 17. (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) (-. (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) ### Axiom
% 1.16/1.34 18. (-. (sdteqdtlpzmzozddtrp0 (xc) (xa) (xq))) (sdteqdtlpzmzozddtrp0 (xc) (xa) (xq)) ### Axiom
% 1.16/1.34 19. ((aInteger0 (xc)) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 (xc) (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 (xc) (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 (xc) (xa) (xq))))) (-. (sdteqdtlpzmzozddtrp0 (xc) (xa) (xq))) ### ConjTree 18
% 1.16/1.34 20. ((aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 (xc)) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 (xc) (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 (xc) (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 (xc) (xa) (xq)))))) (-. (sdteqdtlpzmzozddtrp0 (xc) (xa) (xq))) (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) ### Imply 17 19
% 1.16/1.34 21. (((aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 (xc)) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 (xc) (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 (xc) (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 (xc) (xa) (xq)))))) /\ (((aInteger0 (xc)) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 (xc) (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 (xc) (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 (xc) (xa) (xq))))) => (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))))) (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) (-. (sdteqdtlpzmzozddtrp0 (xc) (xa) (xq))) ### And 20
% 1.16/1.34 22. (All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))) (-. (sdteqdtlpzmzozddtrp0 (xc) (xa) (xq))) (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) ### All 21
% 1.16/1.34 23. (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq)) ### Axiom
% 1.16/1.34 24. (((aInteger0 (xb)) /\ ((aInteger0 (xc)) /\ ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (aInteger0 (xa)))))) => (((sdteqdtlpzmzozddtrp0 (xb) (xc) (xq)) /\ (sdteqdtlpzmzozddtrp0 (xc) (xa) (xq))) => (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq)))) (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) (All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))) (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) => (sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (aInteger0 (xa)) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xc)) (aInteger0 (xb)) ### DisjTree 2 3 4 5 6 16 22 23
% 1.16/1.34 25. (All W3, (((aInteger0 (xb)) /\ ((aInteger0 (xc)) /\ ((aInteger0 (xq)) /\ (((xq) != (sz00)) /\ (aInteger0 W3))))) => (((sdteqdtlpzmzozddtrp0 (xb) (xc) (xq)) /\ (sdteqdtlpzmzozddtrp0 (xc) W3 (xq))) => (sdteqdtlpzmzozddtrp0 (xb) W3 (xq))))) (aInteger0 (xb)) (aInteger0 (xc)) (aInteger0 (xq)) ((xq) != (sz00)) (aInteger0 (xa)) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) => (sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) (All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))) (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) ### All 24
% 1.16/1.34 26. (All W2, (All W3, (((aInteger0 (xb)) /\ ((aInteger0 (xc)) /\ ((aInteger0 W2) /\ ((W2 != (sz00)) /\ (aInteger0 W3))))) => (((sdteqdtlpzmzozddtrp0 (xb) (xc) W2) /\ (sdteqdtlpzmzozddtrp0 (xc) W3 W2)) => (sdteqdtlpzmzozddtrp0 (xb) W3 W2))))) (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) (All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))) (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) => (sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (aInteger0 (xa)) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xc)) (aInteger0 (xb)) ### All 25
% 1.16/1.34 27. (All W1, (All W2, (All W3, (((aInteger0 (xb)) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ ((W2 != (sz00)) /\ (aInteger0 W3))))) => (((sdteqdtlpzmzozddtrp0 (xb) W1 W2) /\ (sdteqdtlpzmzozddtrp0 W1 W3 W2)) => (sdteqdtlpzmzozddtrp0 (xb) W3 W2)))))) (aInteger0 (xb)) (aInteger0 (xc)) (aInteger0 (xq)) ((xq) != (sz00)) (aInteger0 (xa)) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) => (sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) (All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))) (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) ### All 26
% 1.16/1.34 28. (All W0, (All W1, (All W2, (All W3, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ ((W2 != (sz00)) /\ (aInteger0 W3))))) => (((sdteqdtlpzmzozddtrp0 W0 W1 W2) /\ (sdteqdtlpzmzozddtrp0 W1 W3 W2)) => (sdteqdtlpzmzozddtrp0 W0 W3 W2))))))) (-. (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))) (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) (All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))) (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) => (sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (aInteger0 (xa)) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xc)) (aInteger0 (xb)) ### All 27
% 1.16/1.34 29. (-. ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 (xb) (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 (xb) (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))))) (aInteger0 (xb)) (aInteger0 (xc)) (aInteger0 (xq)) ((xq) != (sz00)) (aInteger0 (xa)) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) => (sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) (All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))) (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) (All W0, (All W1, (All W2, (All W3, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ ((W2 != (sz00)) /\ (aInteger0 W3))))) => (((sdteqdtlpzmzozddtrp0 W0 W1 W2) /\ (sdteqdtlpzmzozddtrp0 W1 W3 W2)) => (sdteqdtlpzmzozddtrp0 W0 W3 W2))))))) ### ConjTree 28
% 1.16/1.34 30. (-. (aElementOf0 (xb) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) (aElementOf0 (xb) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) ### Axiom
% 1.16/1.34 31. (((aInteger0 (xb)) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 (xb) (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 (xb) (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))))) => (aElementOf0 (xb) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) (-. (aElementOf0 (xb) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) (All W0, (All W1, (All W2, (All W3, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ ((W2 != (sz00)) /\ (aInteger0 W3))))) => (((sdteqdtlpzmzozddtrp0 W0 W1 W2) /\ (sdteqdtlpzmzozddtrp0 W1 W3 W2)) => (sdteqdtlpzmzozddtrp0 W0 W3 W2))))))) (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) (All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))) (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) => (sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (aInteger0 (xa)) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xc)) (aInteger0 (xb)) ### DisjTree 1 29 30
% 1.16/1.34 32. (((aElementOf0 (xb) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 (xb)) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 (xb) (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 (xb) (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq)))))) /\ (((aInteger0 (xb)) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 (xb) (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 (xb) (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 (xb) (xa) (xq))))) => (aElementOf0 (xb) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))))) (aInteger0 (xb)) (aInteger0 (xc)) (aInteger0 (xq)) ((xq) != (sz00)) (aInteger0 (xa)) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) => (sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) (All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))) (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) (All W0, (All W1, (All W2, (All W3, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ ((W2 != (sz00)) /\ (aInteger0 W3))))) => (((sdteqdtlpzmzozddtrp0 W0 W1 W2) /\ (sdteqdtlpzmzozddtrp0 W1 W3 W2)) => (sdteqdtlpzmzozddtrp0 W0 W3 W2))))))) (-. (aElementOf0 (xb) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) ### And 31
% 1.16/1.34 33. (-. (aElementOf0 (xb) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) (All W0, (All W1, (All W2, (All W3, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ ((W2 != (sz00)) /\ (aInteger0 W3))))) => (((sdteqdtlpzmzozddtrp0 W0 W1 W2) /\ (sdteqdtlpzmzozddtrp0 W1 W3 W2)) => (sdteqdtlpzmzozddtrp0 W0 W3 W2))))))) (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) (All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))) (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) => (sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (aInteger0 (xa)) ((xq) != (sz00)) (aInteger0 (xq)) (aInteger0 (xc)) (aInteger0 (xb)) ### All 32
% 1.16/1.34 34. (-. (((aSet0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) /\ ((All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))) /\ ((-. (aElementOf0 (xb) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) /\ ((aElementOf0 (xb) (stldt0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) /\ ((Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xc) (smndt0 (xb)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 (xc) (smndt0 (xb)))) /\ (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)))))))) => (((aSet0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) /\ (All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))))))) => ((-. (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) \/ (aElementOf0 (xc) (stldt0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))))) (aInteger0 (xb)) (aInteger0 (xc)) (aInteger0 (xq)) ((xq) != (sz00)) (aInteger0 (xa)) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) => (sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (All W0, (All W1, (All W2, (All W3, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ ((W2 != (sz00)) /\ (aInteger0 W3))))) => (((sdteqdtlpzmzozddtrp0 W0 W1 W2) /\ (sdteqdtlpzmzozddtrp0 W1 W3 W2)) => (sdteqdtlpzmzozddtrp0 W0 W3 W2))))))) ### ConjTree 33
% 1.16/1.34 35. ((aInteger0 (xb)) /\ (aInteger0 (xc))) (All W0, (All W1, (All W2, (All W3, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ ((W2 != (sz00)) /\ (aInteger0 W3))))) => (((sdteqdtlpzmzozddtrp0 W0 W1 W2) /\ (sdteqdtlpzmzozddtrp0 W1 W3 W2)) => (sdteqdtlpzmzozddtrp0 W0 W3 W2))))))) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) => (sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (aInteger0 (xa)) ((xq) != (sz00)) (aInteger0 (xq)) (-. (((aSet0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) /\ ((All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))) /\ ((-. (aElementOf0 (xb) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) /\ ((aElementOf0 (xb) (stldt0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) /\ ((Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xc) (smndt0 (xb)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 (xc) (smndt0 (xb)))) /\ (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)))))))) => (((aSet0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) /\ (All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))))))) => ((-. (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) \/ (aElementOf0 (xc) (stldt0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))))) ### And 34
% 1.16/1.34 36. ((aInteger0 (xa)) /\ ((aInteger0 (xq)) /\ ((xq) != (sz00)))) (-. (((aSet0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) /\ ((All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))) /\ ((-. (aElementOf0 (xb) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) /\ ((aElementOf0 (xb) (stldt0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) /\ ((Ex W0, ((aInteger0 W0) /\ ((sdtasdt0 (xq) W0) = (sdtpldt0 (xc) (smndt0 (xb)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 (xc) (smndt0 (xb)))) /\ (sdteqdtlpzmzozddtrp0 (xc) (xb) (xq)))))))) => (((aSet0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) /\ (All W0, (((aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))) => ((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) /\ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) /\ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq)))))) /\ (((aInteger0 W0) /\ ((Ex W1, ((aInteger0 W1) /\ ((sdtasdt0 (xq) W1) = (sdtpldt0 W0 (smndt0 (xa)))))) \/ ((aDivisorOf0 (xq) (sdtpldt0 W0 (smndt0 (xa)))) \/ (sdteqdtlpzmzozddtrp0 W0 (xa) (xq))))) => (aElementOf0 W0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq))))))) => ((-. (aElementOf0 (xc) (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))) \/ (aElementOf0 (xc) (stldt0 (szAzrzSzezqlpdtcmdtrp0 (xa) (xq)))))))) (All W0, (All W1, (All W2, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ (W2 != (sz00))))) => ((sdteqdtlpzmzozddtrp0 W0 W1 W2) => (sdteqdtlpzmzozddtrp0 W1 W0 W2)))))) (All W0, (All W1, (All W2, (All W3, (((aInteger0 W0) /\ ((aInteger0 W1) /\ ((aInteger0 W2) /\ ((W2 != (sz00)) /\ (aInteger0 W3))))) => (((sdteqdtlpzmzozddtrp0 W0 W1 W2) /\ (sdteqdtlpzmzozddtrp0 W1 W3 W2)) => (sdteqdtlpzmzozddtrp0 W0 W3 W2))))))) ((aInteger0 (xb)) /\ (aInteger0 (xc))) ### ConjTree 35
% 1.16/1.34 % SZS output end Proof
% 1.16/1.34 (* END-PROOF *)
%------------------------------------------------------------------------------