TSTP Solution File: RNG088+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : RNG088+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 : 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 : Mon Jul 18 20:41:57 EDT 2022
% Result : Theorem 37.83s 38.08s
% Output : Proof 37.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG088+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon May 30 22:22:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 37.83/38.08 % SZS status Theorem
% 37.83/38.08 (* PROOF-FOUND *)
% 37.83/38.08 (* BEGIN-PROOF *)
% 37.83/38.08 % SZS output start Proof
% 37.83/38.08 1. (aElementOf0 (xk) (xI)) (-. (aElementOf0 (xk) (xI))) ### Axiom
% 37.83/38.08 2. (aElementOf0 (xm) (xI)) (-. (aElementOf0 (xm) (xI))) ### Axiom
% 37.83/38.08 3. (-. (aElementOf0 (sdtpldt0 (xk) (xm)) (xI))) (aElementOf0 (sdtpldt0 (xk) (xm)) (xI)) ### Axiom
% 37.83/38.08 4. ((aElementOf0 (xm) (xI)) => (aElementOf0 (sdtpldt0 (xk) (xm)) (xI))) (-. (aElementOf0 (sdtpldt0 (xk) (xm)) (xI))) (aElementOf0 (xm) (xI)) ### Imply 2 3
% 37.83/38.08 5. (All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 (xk) W2) (xI)))) (aElementOf0 (xm) (xI)) (-. (aElementOf0 (sdtpldt0 (xk) (xm)) (xI))) ### All 4
% 37.83/38.08 6. ((All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 (xk) W2) (xI)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 (xk)) (xI))))) (-. (aElementOf0 (sdtpldt0 (xk) (xm)) (xI))) (aElementOf0 (xm) (xI)) ### And 5
% 37.83/38.08 7. ((aElementOf0 (xk) (xI)) => ((All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 (xk) W2) (xI)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 (xk)) (xI)))))) (aElementOf0 (xm) (xI)) (-. (aElementOf0 (sdtpldt0 (xk) (xm)) (xI))) (aElementOf0 (xk) (xI)) ### Imply 1 6
% 37.83/38.08 8. (All W1, ((aElementOf0 W1 (xI)) => ((All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 W1 W2) (xI)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (xI))))))) (aElementOf0 (xk) (xI)) (-. (aElementOf0 (sdtpldt0 (xk) (xm)) (xI))) (aElementOf0 (xm) (xI)) ### All 7
% 37.83/38.08 9. (aElementOf0 (xl) (xJ)) (-. (aElementOf0 (xl) (xJ))) ### Axiom
% 37.83/38.08 10. (aElementOf0 (xn) (xJ)) (-. (aElementOf0 (xn) (xJ))) ### Axiom
% 37.83/38.08 11. (-. (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ))) (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ)) ### Axiom
% 37.83/38.08 12. ((aElementOf0 (xn) (xJ)) => (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ))) (-. (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ))) (aElementOf0 (xn) (xJ)) ### Imply 10 11
% 37.83/38.08 13. (All W2, ((aElementOf0 W2 (xJ)) => (aElementOf0 (sdtpldt0 (xl) W2) (xJ)))) (aElementOf0 (xn) (xJ)) (-. (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ))) ### All 12
% 37.83/38.08 14. ((All W2, ((aElementOf0 W2 (xJ)) => (aElementOf0 (sdtpldt0 (xl) W2) (xJ)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 (xl)) (xJ))))) (-. (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ))) (aElementOf0 (xn) (xJ)) ### And 13
% 37.83/38.08 15. ((aElementOf0 (xl) (xJ)) => ((All W2, ((aElementOf0 W2 (xJ)) => (aElementOf0 (sdtpldt0 (xl) W2) (xJ)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 (xl)) (xJ)))))) (aElementOf0 (xn) (xJ)) (-. (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ))) (aElementOf0 (xl) (xJ)) ### Imply 9 14
% 37.83/38.08 16. (All W1, ((aElementOf0 W1 (xJ)) => ((All W2, ((aElementOf0 W2 (xJ)) => (aElementOf0 (sdtpldt0 W1 W2) (xJ)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (xJ))))))) (aElementOf0 (xl) (xJ)) (-. (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ))) (aElementOf0 (xn) (xJ)) ### All 15
% 37.83/38.08 17. (-. ((aElementOf0 (sdtpldt0 (xk) (xm)) (xI)) /\ (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ)))) (aElementOf0 (xn) (xJ)) (aElementOf0 (xl) (xJ)) (All W1, ((aElementOf0 W1 (xJ)) => ((All W2, ((aElementOf0 W2 (xJ)) => (aElementOf0 (sdtpldt0 W1 W2) (xJ)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (xJ))))))) (aElementOf0 (xm) (xI)) (aElementOf0 (xk) (xI)) (All W1, ((aElementOf0 W1 (xI)) => ((All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 W1 W2) (xI)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (xI))))))) ### NotAnd 8 16
% 37.83/38.08 18. ((aSet0 (xJ)) /\ (All W1, ((aElementOf0 W1 (xJ)) => ((All W2, ((aElementOf0 W2 (xJ)) => (aElementOf0 (sdtpldt0 W1 W2) (xJ)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (xJ)))))))) (All W1, ((aElementOf0 W1 (xI)) => ((All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 W1 W2) (xI)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (xI))))))) (aElementOf0 (xk) (xI)) (aElementOf0 (xm) (xI)) (aElementOf0 (xl) (xJ)) (aElementOf0 (xn) (xJ)) (-. ((aElementOf0 (sdtpldt0 (xk) (xm)) (xI)) /\ (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ)))) ### And 17
% 37.83/38.08 19. (aIdeal0 (xJ)) (-. ((aElementOf0 (sdtpldt0 (xk) (xm)) (xI)) /\ (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ)))) (aElementOf0 (xn) (xJ)) (aElementOf0 (xl) (xJ)) (aElementOf0 (xm) (xI)) (aElementOf0 (xk) (xI)) (All W1, ((aElementOf0 W1 (xI)) => ((All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 W1 W2) (xI)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (xI))))))) ### Definition-Pseudo(aIdeal0) 18
% 37.83/38.08 20. ((aSet0 (xI)) /\ (All W1, ((aElementOf0 W1 (xI)) => ((All W2, ((aElementOf0 W2 (xI)) => (aElementOf0 (sdtpldt0 W1 W2) (xI)))) /\ (All W2, ((aElement0 W2) => (aElementOf0 (sdtasdt0 W2 W1) (xI)))))))) (aElementOf0 (xk) (xI)) (aElementOf0 (xm) (xI)) (aElementOf0 (xl) (xJ)) (aElementOf0 (xn) (xJ)) (-. ((aElementOf0 (sdtpldt0 (xk) (xm)) (xI)) /\ (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ)))) (aIdeal0 (xJ)) ### And 19
% 37.83/38.08 21. (aIdeal0 (xI)) (aIdeal0 (xJ)) (-. ((aElementOf0 (sdtpldt0 (xk) (xm)) (xI)) /\ (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ)))) (aElementOf0 (xn) (xJ)) (aElementOf0 (xl) (xJ)) (aElementOf0 (xm) (xI)) (aElementOf0 (xk) (xI)) ### Definition-Pseudo(aIdeal0) 20
% 37.83/38.08 22. ((aIdeal0 (xI)) /\ (aIdeal0 (xJ))) (aElementOf0 (xk) (xI)) (aElementOf0 (xm) (xI)) (aElementOf0 (xl) (xJ)) (aElementOf0 (xn) (xJ)) (-. ((aElementOf0 (sdtpldt0 (xk) (xm)) (xI)) /\ (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ)))) ### And 21
% 37.83/38.08 23. ((aElementOf0 (xk) (xI)) /\ ((aElementOf0 (xl) (xJ)) /\ ((xx) = (sdtpldt0 (xk) (xl))))) (-. ((aElementOf0 (sdtpldt0 (xk) (xm)) (xI)) /\ (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ)))) (aElementOf0 (xn) (xJ)) (aElementOf0 (xm) (xI)) ((aIdeal0 (xI)) /\ (aIdeal0 (xJ))) ### ConjTree 22
% 37.83/38.08 24. ((aElementOf0 (xm) (xI)) /\ ((aElementOf0 (xn) (xJ)) /\ ((xy) = (sdtpldt0 (xm) (xn))))) ((aIdeal0 (xI)) /\ (aIdeal0 (xJ))) (-. ((aElementOf0 (sdtpldt0 (xk) (xm)) (xI)) /\ (aElementOf0 (sdtpldt0 (xl) (xn)) (xJ)))) ((aElementOf0 (xk) (xI)) /\ ((aElementOf0 (xl) (xJ)) /\ ((xx) = (sdtpldt0 (xk) (xl))))) ### ConjTree 23
% 37.83/38.08 % SZS output end Proof
% 37.83/38.08 (* END-PROOF *)
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