TSTP Solution File: RNG111+4 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : RNG111+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 : n018.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 20:42:01 EDT 2022
% Result : Theorem 2.38s 2.59s
% Output : Proof 2.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG111+4 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 10:02:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.38/2.59 % SZS status Theorem
% 2.38/2.59 (* PROOF-FOUND *)
% 2.38/2.59 (* BEGIN-PROOF *)
% 2.38/2.59 % SZS output start Proof
% 2.38/2.59 1. (Ex W1, (Ex W2, ((aElementOf0 W1 (slsdtgt0 (xa))) /\ ((aElementOf0 W2 (slsdtgt0 (xb))) /\ ((sdtpldt0 W1 W2) = T_0))))) (-. (Ex W1, (Ex W2, ((aElementOf0 W1 (slsdtgt0 (xa))) /\ ((aElementOf0 W2 (slsdtgt0 (xb))) /\ ((sdtpldt0 W1 W2) = T_0)))))) ### Axiom
% 2.38/2.59 2. (-. ((Ex W1, (Ex W2, ((aElementOf0 W1 (slsdtgt0 (xa))) /\ ((aElementOf0 W2 (slsdtgt0 (xb))) /\ ((sdtpldt0 W1 W2) = T_0))))) \/ (aElementOf0 T_0 (xI)))) (Ex W1, (Ex W2, ((aElementOf0 W1 (slsdtgt0 (xa))) /\ ((aElementOf0 W2 (slsdtgt0 (xb))) /\ ((sdtpldt0 W1 W2) = T_0))))) ### NotOr 1
% 2.38/2.59 3. (T_0 != (sz00)) (T_0 = (sz00)) ### Axiom
% 2.38/2.59 4. (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_1))))) (-. (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_1)))))) ### Axiom
% 2.38/2.59 5. (-. ((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_1))))) \/ (aElementOf0 T_1 (xI)))) (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_1))))) ### NotOr 4
% 2.38/2.59 6. (T_1 != (sz00)) (T_1 = (sz00)) ### Axiom
% 2.38/2.59 7. (iLess0 (sbrdtbr0 T_1) (sbrdtbr0 T_0)) (-. (iLess0 (sbrdtbr0 T_1) (sbrdtbr0 T_0))) ### Axiom
% 2.38/2.59 8. (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_2))))) (-. (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_2)))))) ### Axiom
% 2.38/2.59 9. (-. ((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_2))))) \/ (aElementOf0 T_2 (xI)))) (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_2))))) ### NotOr 8
% 2.38/2.59 10. (T_2 != (sz00)) (T_2 = (sz00)) ### Axiom
% 2.38/2.59 11. (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_3))))) (-. (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_3)))))) ### Axiom
% 2.38/2.59 12. (-. ((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_3))))) \/ (aElementOf0 T_3 (xI)))) (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_3))))) ### NotOr 11
% 2.38/2.59 13. (T_3 != (sz00)) (T_3 = (sz00)) ### Axiom
% 2.38/2.59 14. (iLess0 (sbrdtbr0 T_3) (sbrdtbr0 T_2)) (-. (iLess0 (sbrdtbr0 T_3) (sbrdtbr0 T_2))) ### Axiom
% 2.38/2.59 15. ((((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_3))))) \/ (aElementOf0 T_3 (xI))) /\ (T_3 != (sz00))) => (-. (iLess0 (sbrdtbr0 T_3) (sbrdtbr0 T_2)))) (iLess0 (sbrdtbr0 T_3) (sbrdtbr0 T_2)) (T_3 != (sz00)) (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_3))))) ### DisjTree 12 13 14
% 2.38/2.59 16. (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 T_2))))) (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_3))))) (T_3 != (sz00)) (iLess0 (sbrdtbr0 T_3) (sbrdtbr0 T_2)) ### All 15
% 2.38/2.59 17. (-. (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_3))))) /\ ((aElementOf0 T_3 (xI)) /\ (T_3 != (sz00)))) => (-. (iLess0 (sbrdtbr0 T_3) (sbrdtbr0 T_2))))) (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 T_2))))) ### ConjTree 16
% 2.38/2.59 18. (-. (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 T_2)))))) (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 T_2))))) ### NotAllEx 17
% 2.38/2.59 19. (-. (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_2))))) \/ (aElementOf0 T_2 (xI))) /\ ((T_2 != (sz00)) /\ (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 T_2)))))))) (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 T_2))))) (T_2 != (sz00)) (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_2))))) ### DisjTree 9 10 18
% 2.38/2.59 20. (-. (Ex W1, (((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ ((W1 != (sz00)) /\ (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1))))))))) (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_2))))) (T_2 != (sz00)) (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 T_2))))) ### NotExists 19
% 2.38/2.59 21. ((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_2))))) /\ ((aElementOf0 T_2 (xI)) /\ ((T_2 != (sz00)) /\ (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 T_2)))))))) (-. (Ex W1, (((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ ((W1 != (sz00)) /\ (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1))))))))) ### ConjTree 20
% 2.38/2.59 22. (Ex W2, ((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ ((W2 != (sz00)) /\ (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2))))))))) (-. (Ex W1, (((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ ((W1 != (sz00)) /\ (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1))))))))) ### Exists 21
% 2.38/2.59 23. ((((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_1))))) \/ (aElementOf0 T_1 (xI))) /\ (T_1 != (sz00))) => ((iLess0 (sbrdtbr0 T_1) (sbrdtbr0 T_0)) => (Ex W2, ((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ ((W2 != (sz00)) /\ (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2))))))))))) (-. (Ex W1, (((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ ((W1 != (sz00)) /\ (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1))))))))) (iLess0 (sbrdtbr0 T_1) (sbrdtbr0 T_0)) (T_1 != (sz00)) (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_1))))) ### DisjTree 5 6 7 22
% 2.43/2.62 24. (All W1, ((((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ (W1 != (sz00))) => ((iLess0 (sbrdtbr0 W1) (sbrdtbr0 T_0)) => (Ex W2, ((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ ((W2 != (sz00)) /\ (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2)))))))))))) (Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_1))))) (T_1 != (sz00)) (iLess0 (sbrdtbr0 T_1) (sbrdtbr0 T_0)) (-. (Ex W1, (((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ ((W1 != (sz00)) /\ (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1))))))))) ### All 23
% 2.43/2.62 25. (-. (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = T_1))))) /\ ((aElementOf0 T_1 (xI)) /\ (T_1 != (sz00)))) => (-. (iLess0 (sbrdtbr0 T_1) (sbrdtbr0 T_0))))) (-. (Ex W1, (((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ ((W1 != (sz00)) /\ (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1))))))))) (All W1, ((((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ (W1 != (sz00))) => ((iLess0 (sbrdtbr0 W1) (sbrdtbr0 T_0)) => (Ex W2, ((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ ((W2 != (sz00)) /\ (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2)))))))))))) ### ConjTree 24
% 2.43/2.62 26. (-. (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 T_0)))))) (All W1, ((((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ (W1 != (sz00))) => ((iLess0 (sbrdtbr0 W1) (sbrdtbr0 T_0)) => (Ex W2, ((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ ((W2 != (sz00)) /\ (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2)))))))))))) (-. (Ex W1, (((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ ((W1 != (sz00)) /\ (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1))))))))) ### NotAllEx 25
% 2.43/2.62 27. (-. (((Ex W1, (Ex W2, ((aElementOf0 W1 (slsdtgt0 (xa))) /\ ((aElementOf0 W2 (slsdtgt0 (xb))) /\ ((sdtpldt0 W1 W2) = T_0))))) \/ (aElementOf0 T_0 (xI))) /\ ((T_0 != (sz00)) /\ (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 T_0)))))))) (-. (Ex W1, (((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ ((W1 != (sz00)) /\ (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1))))))))) (All W1, ((((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ (W1 != (sz00))) => ((iLess0 (sbrdtbr0 W1) (sbrdtbr0 T_0)) => (Ex W2, ((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ ((W2 != (sz00)) /\ (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2)))))))))))) (T_0 != (sz00)) (Ex W1, (Ex W2, ((aElementOf0 W1 (slsdtgt0 (xa))) /\ ((aElementOf0 W2 (slsdtgt0 (xb))) /\ ((sdtpldt0 W1 W2) = T_0))))) ### DisjTree 2 3 26
% 2.43/2.62 28. (Ex W1, (Ex W2, ((aElementOf0 W1 (slsdtgt0 (xa))) /\ ((aElementOf0 W2 (slsdtgt0 (xb))) /\ ((sdtpldt0 W1 W2) = T_0))))) (T_0 != (sz00)) (All W1, ((((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ (W1 != (sz00))) => ((iLess0 (sbrdtbr0 W1) (sbrdtbr0 T_0)) => (Ex W2, ((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ ((W2 != (sz00)) /\ (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2)))))))))))) (-. (Ex W1, (((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ ((W1 != (sz00)) /\ (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1))))))))) ### NotExists 27
% 2.43/2.62 29. (-. (((Ex W1, (Ex W2, ((aElementOf0 W1 (slsdtgt0 (xa))) /\ ((aElementOf0 W2 (slsdtgt0 (xb))) /\ ((sdtpldt0 W1 W2) = T_0))))) /\ ((aElementOf0 T_0 (xI)) /\ (T_0 != (sz00)))) => ((All W1, ((((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ (W1 != (sz00))) => ((iLess0 (sbrdtbr0 W1) (sbrdtbr0 T_0)) => (Ex W2, ((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ ((W2 != (sz00)) /\ (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2)))))))))))) => (Ex W1, (((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ ((W1 != (sz00)) /\ (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1))))))))))) ### ConjTree 28
% 2.43/2.62 30. (-. (All W0, (((Ex W1, (Ex W2, ((aElementOf0 W1 (slsdtgt0 (xa))) /\ ((aElementOf0 W2 (slsdtgt0 (xb))) /\ ((sdtpldt0 W1 W2) = W0))))) /\ ((aElementOf0 W0 (xI)) /\ (W0 != (sz00)))) => ((All W1, ((((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ (W1 != (sz00))) => ((iLess0 (sbrdtbr0 W1) (sbrdtbr0 W0)) => (Ex W2, ((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ ((W2 != (sz00)) /\ (All W3, ((((Ex W4, (Ex W5, ((aElementOf0 W4 (slsdtgt0 (xa))) /\ ((aElementOf0 W5 (slsdtgt0 (xb))) /\ ((sdtpldt0 W4 W5) = W3))))) \/ (aElementOf0 W3 (xI))) /\ (W3 != (sz00))) => (-. (iLess0 (sbrdtbr0 W3) (sbrdtbr0 W2)))))))))))) => (Ex W1, (((Ex W2, (Ex W3, ((aElementOf0 W2 (slsdtgt0 (xa))) /\ ((aElementOf0 W3 (slsdtgt0 (xb))) /\ ((sdtpldt0 W2 W3) = W1))))) \/ (aElementOf0 W1 (xI))) /\ ((W1 != (sz00)) /\ (All W2, (((Ex W3, (Ex W4, ((aElementOf0 W3 (slsdtgt0 (xa))) /\ ((aElementOf0 W4 (slsdtgt0 (xb))) /\ ((sdtpldt0 W3 W4) = W2))))) /\ ((aElementOf0 W2 (xI)) /\ (W2 != (sz00)))) => (-. (iLess0 (sbrdtbr0 W2) (sbrdtbr0 W1)))))))))))) ### NotAllEx 29
% 2.43/2.62 % SZS output end Proof
% 2.43/2.62 (* END-PROOF *)
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