TSTP Solution File: RNG067+1 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : RNG067+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 : n020.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 20:41:55 EDT 2022
% Result : Theorem 0.18s 0.51s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG067+1 : 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 : n020.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 15:04:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.51 % SZS status Theorem
% 0.18/0.51 (* PROOF-FOUND *)
% 0.18/0.51 (* BEGIN-PROOF *)
% 0.18/0.51 % SZS output start Proof
% 0.18/0.51 1. (aScalar0 (xP)) (-. (aScalar0 (xP))) ### Axiom
% 0.18/0.51 2. (aScalar0 (xP)) (-. (aScalar0 (xP))) ### Axiom
% 0.18/0.51 3. (-. (aScalar0 (sdtasdt0 (xP) (xP)))) (aScalar0 (xP)) ### Extension/test/mMulScctrp 1 2
% 0.18/0.51 4. (-. (aScalar0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))))) (aScalar0 (xP)) ### Extension/test/mSumScctrp 3 3
% 0.18/0.51 5. (-. (aScalar0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))))) (aScalar0 (xP)) ### Extension/test/mSumScctrp 4 3
% 0.18/0.51 6. (aScalar0 (xR)) (-. (aScalar0 (xR))) ### Axiom
% 0.18/0.51 7. (aScalar0 (xR)) (-. (aScalar0 (xR))) ### Axiom
% 0.18/0.51 8. (-. (aScalar0 (sdtasdt0 (xR) (xR)))) (aScalar0 (xR)) ### Extension/test/mMulScctrp 6 7
% 0.18/0.51 9. (aScalar0 (xS)) (-. (aScalar0 (xS))) ### Axiom
% 0.18/0.51 10. (aScalar0 (xS)) (-. (aScalar0 (xS))) ### Axiom
% 0.18/0.51 11. (-. (aScalar0 (sdtasdt0 (xS) (xS)))) (aScalar0 (xS)) ### Extension/test/mMulScctrp 9 10
% 0.18/0.51 12. (-. (aScalar0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))))) (aScalar0 (xS)) (aScalar0 (xR)) ### Extension/test/mSumScctrp 8 11
% 0.18/0.51 13. (aScalar0 (xN)) (-. (aScalar0 (xN))) ### Axiom
% 0.18/0.51 14. (-. (aScalar0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)))) (aScalar0 (xN)) (aScalar0 (xR)) (aScalar0 (xS)) ### Extension/test/mSumScctrp 12 13
% 0.18/0.51 15. (aScalar0 (xN)) (-. (aScalar0 (xN))) ### Axiom
% 0.18/0.51 16. (aScalar0 (xN)) (-. (aScalar0 (xN))) ### Axiom
% 0.18/0.51 17. (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (-. (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))))) ### Axiom
% 0.18/0.51 18. (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (-. (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN))) ### Axiom
% 0.18/0.51 19. (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)))) (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN))) ### Axiom
% 0.18/0.51 20. (((aScalar0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP)))) /\ ((aScalar0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) /\ ((aScalar0 (sdtasdt0 (xP) (xP))) /\ (aScalar0 (xN))))) => (((sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) /\ (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN))) => (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN))))) (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (aScalar0 (xN)) (aScalar0 (xR)) (aScalar0 (xS)) (aScalar0 (xP)) ### DisjTree 4 12 3 16 17 18 19
% 0.18/0.51 21. (All W3, (((aScalar0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP)))) /\ ((aScalar0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) /\ ((aScalar0 (sdtasdt0 (xP) (xP))) /\ (aScalar0 W3)))) => (((sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) /\ (sdtlseqdt0 (sdtasdt0 (xP) (xP)) W3)) => (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) W3))))) (aScalar0 (xP)) (aScalar0 (xS)) (aScalar0 (xR)) (aScalar0 (xN)) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)))) ### All 20
% 0.18/0.51 22. (All W2, (All W3, (((aScalar0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP)))) /\ ((aScalar0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) W2) (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) W3)))))) (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (aScalar0 (xN)) (aScalar0 (xR)) (aScalar0 (xS)) (aScalar0 (xP)) ### All 21
% 0.18/0.51 23. (All W1, (All W2, (All W3, (((aScalar0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP)))) /\ ((aScalar0 W1) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) W1) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) W2) (sdtpldt0 W1 W3))))))) (aScalar0 (xP)) (aScalar0 (xS)) (aScalar0 (xR)) (aScalar0 (xN)) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)))) ### All 22
% 0.18/0.51 24. (All W0, (All W1, (All W2, (All W3, (((aScalar0 W0) /\ ((aScalar0 W1) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 W0 W1) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 W0 W2) (sdtpldt0 W1 W3)))))))) (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (aScalar0 (xN)) (aScalar0 (xR)) (aScalar0 (xS)) (aScalar0 (xP)) ### All 23
% 0.18/0.51 25. (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (-. (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN))) ### Axiom
% 0.18/0.51 26. (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) (xN)))) (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) (xN))) ### Axiom
% 0.18/0.51 27. (((aScalar0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP)))) /\ ((aScalar0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN))) /\ ((aScalar0 (sdtasdt0 (xP) (xP))) /\ (aScalar0 (xN))))) => (((sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN))) /\ (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN))) => (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) (xN))))) (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) (xN)))) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (All W0, (All W1, (All W2, (All W3, (((aScalar0 W0) /\ ((aScalar0 W1) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 W0 W1) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 W0 W2) (sdtpldt0 W1 W3)))))))) (aScalar0 (xS)) (aScalar0 (xR)) (aScalar0 (xN)) (aScalar0 (xP)) ### DisjTree 5 14 3 15 24 25 26
% 0.18/0.51 28. (All W3, (((aScalar0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP)))) /\ ((aScalar0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN))) /\ ((aScalar0 (sdtasdt0 (xP) (xP))) /\ (aScalar0 W3)))) => (((sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN))) /\ (sdtlseqdt0 (sdtasdt0 (xP) (xP)) W3)) => (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) W3))))) (aScalar0 (xP)) (aScalar0 (xN)) (aScalar0 (xR)) (aScalar0 (xS)) (All W0, (All W1, (All W2, (All W3, (((aScalar0 W0) /\ ((aScalar0 W1) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 W0 W1) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 W0 W2) (sdtpldt0 W1 W3)))))))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) (xN)))) ### All 27
% 0.18/0.51 29. (All W2, (All W3, (((aScalar0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP)))) /\ ((aScalar0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN))) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN))) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) W2) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) W3)))))) (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) (xN)))) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (All W0, (All W1, (All W2, (All W3, (((aScalar0 W0) /\ ((aScalar0 W1) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 W0 W1) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 W0 W2) (sdtpldt0 W1 W3)))))))) (aScalar0 (xS)) (aScalar0 (xR)) (aScalar0 (xN)) (aScalar0 (xP)) ### All 28
% 0.18/0.51 30. (All W1, (All W2, (All W3, (((aScalar0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP)))) /\ ((aScalar0 W1) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) W1) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) W2) (sdtpldt0 W1 W3))))))) (aScalar0 (xP)) (aScalar0 (xN)) (aScalar0 (xR)) (aScalar0 (xS)) (All W0, (All W1, (All W2, (All W3, (((aScalar0 W0) /\ ((aScalar0 W1) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 W0 W1) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 W0 W2) (sdtpldt0 W1 W3)))))))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) (xN)))) ### All 29
% 0.18/0.51 31. (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) (xN)))) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (All W0, (All W1, (All W2, (All W3, (((aScalar0 W0) /\ ((aScalar0 W1) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 W0 W1) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 W0 W2) (sdtpldt0 W1 W3)))))))) (aScalar0 (xS)) (aScalar0 (xR)) (aScalar0 (xN)) (aScalar0 (xP)) ### All 30
% 0.18/0.51 32. ((aScalar0 (xN)) /\ ((xN) = (sdtasdt0 (xR) (xS)))) (aScalar0 (xP)) (aScalar0 (xR)) (aScalar0 (xS)) (All W0, (All W1, (All W2, (All W3, (((aScalar0 W0) /\ ((aScalar0 W1) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 W0 W1) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 W0 W2) (sdtpldt0 W1 W3)))))))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) (xN)))) ### And 31
% 0.18/0.51 33. ((aScalar0 (xS)) /\ ((xS) = (sdtasdt0 (xF) (xD)))) (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) (xN)))) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (All W0, (All W1, (All W2, (All W3, (((aScalar0 W0) /\ ((aScalar0 W1) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 W0 W1) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 W0 W2) (sdtpldt0 W1 W3)))))))) (aScalar0 (xR)) (aScalar0 (xP)) ((aScalar0 (xN)) /\ ((xN) = (sdtasdt0 (xR) (xS)))) ### And 32
% 0.18/0.51 34. ((aScalar0 (xP)) /\ ((xP) = (sdtasdt0 (xE) (xH)))) ((aScalar0 (xN)) /\ ((xN) = (sdtasdt0 (xR) (xS)))) (aScalar0 (xR)) (All W0, (All W1, (All W2, (All W3, (((aScalar0 W0) /\ ((aScalar0 W1) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 W0 W1) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 W0 W2) (sdtpldt0 W1 W3)))))))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) (xN)))) ((aScalar0 (xS)) /\ ((xS) = (sdtasdt0 (xF) (xD)))) ### And 33
% 0.18/0.51 35. ((aScalar0 (xR)) /\ ((xR) = (sdtasdt0 (xC) (xG)))) ((aScalar0 (xS)) /\ ((xS) = (sdtasdt0 (xF) (xD)))) (-. (sdtlseqdt0 (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtpldt0 (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS))) (xN)) (xN)))) (sdtlseqdt0 (sdtpldt0 (sdtasdt0 (xP) (xP)) (sdtasdt0 (xP) (xP))) (sdtpldt0 (sdtasdt0 (xR) (xR)) (sdtasdt0 (xS) (xS)))) (sdtlseqdt0 (sdtasdt0 (xP) (xP)) (xN)) (All W0, (All W1, (All W2, (All W3, (((aScalar0 W0) /\ ((aScalar0 W1) /\ ((aScalar0 W2) /\ (aScalar0 W3)))) => (((sdtlseqdt0 W0 W1) /\ (sdtlseqdt0 W2 W3)) => (sdtlseqdt0 (sdtpldt0 W0 W2) (sdtpldt0 W1 W3)))))))) ((aScalar0 (xN)) /\ ((xN) = (sdtasdt0 (xR) (xS)))) ((aScalar0 (xP)) /\ ((xP) = (sdtasdt0 (xE) (xH)))) ### And 34
% 0.18/0.51 % SZS output end Proof
% 0.18/0.51 (* END-PROOF *)
%------------------------------------------------------------------------------