%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : COM018+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 : n032.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 : Fri Jul 15 01:45:52 EDT 2022 % Result : Theorem 0.61s 0.80s % Output : Proof 0.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : COM018+4 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.11/0.32 % Computer : n032.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Thu Jun 16 17:41:15 EDT 2022 % 0.11/0.32 % CPUTime : % 0.61/0.80 % SZS status Theorem % 0.61/0.80 (* PROOF-FOUND *) % 0.61/0.80 (* BEGIN-PROOF *) % 0.61/0.80 % SZS output start Proof % 0.61/0.80 1. (aRewritingSystem0 (xR)) (-. (aRewritingSystem0 (xR))) ### Axiom % 0.61/0.80 2. (isTerminating0 (xR)) (-. (isTerminating0 (xR))) ### Axiom % 0.61/0.80 3. (aElement0 (xw)) (-. (aElement0 (xw))) ### Axiom % 0.61/0.80 4. (aNormalFormOfIn0 T_0 (xw) (xR)) (-. (aNormalFormOfIn0 T_0 (xw) (xR))) ### Axiom % 0.61/0.80 5. (-. (((aElement0 T_0) /\ ((((xw) = T_0) \/ ((aReductOfIn0 T_0 (xw) (xR)) \/ ((Ex W1, ((aElement0 W1) /\ ((aReductOfIn0 W1 (xw) (xR)) /\ (sdtmndtplgtdt0 W1 (xR) T_0)))) \/ ((sdtmndtplgtdt0 (xw) (xR) T_0) \/ (sdtmndtasgtdt0 (xw) (xR) T_0))))) /\ (-. (Ex W1, (aReductOfIn0 W1 T_0 (xR)))))) \/ (aNormalFormOfIn0 T_0 (xw) (xR)))) (aNormalFormOfIn0 T_0 (xw) (xR)) ### NotOr 4 % 0.61/0.80 6. (-. (Ex W0, (((aElement0 W0) /\ ((((xw) = W0) \/ ((aReductOfIn0 W0 (xw) (xR)) \/ ((Ex W1, ((aElement0 W1) /\ ((aReductOfIn0 W1 (xw) (xR)) /\ (sdtmndtplgtdt0 W1 (xR) W0)))) \/ ((sdtmndtplgtdt0 (xw) (xR) W0) \/ (sdtmndtasgtdt0 (xw) (xR) W0))))) /\ (-. (Ex W1, (aReductOfIn0 W1 W0 (xR)))))) \/ (aNormalFormOfIn0 W0 (xw) (xR))))) (aNormalFormOfIn0 T_0 (xw) (xR)) ### NotExists 5 % 0.61/0.80 7. (Ex W2, (aNormalFormOfIn0 W2 (xw) (xR))) (-. (Ex W0, (((aElement0 W0) /\ ((((xw) = W0) \/ ((aReductOfIn0 W0 (xw) (xR)) \/ ((Ex W1, ((aElement0 W1) /\ ((aReductOfIn0 W1 (xw) (xR)) /\ (sdtmndtplgtdt0 W1 (xR) W0)))) \/ ((sdtmndtplgtdt0 (xw) (xR) W0) \/ (sdtmndtasgtdt0 (xw) (xR) W0))))) /\ (-. (Ex W1, (aReductOfIn0 W1 W0 (xR)))))) \/ (aNormalFormOfIn0 W0 (xw) (xR))))) ### Exists 6 % 0.61/0.80 8. ((aElement0 (xw)) => (Ex W2, (aNormalFormOfIn0 W2 (xw) (xR)))) (-. (Ex W0, (((aElement0 W0) /\ ((((xw) = W0) \/ ((aReductOfIn0 W0 (xw) (xR)) \/ ((Ex W1, ((aElement0 W1) /\ ((aReductOfIn0 W1 (xw) (xR)) /\ (sdtmndtplgtdt0 W1 (xR) W0)))) \/ ((sdtmndtplgtdt0 (xw) (xR) W0) \/ (sdtmndtasgtdt0 (xw) (xR) W0))))) /\ (-. (Ex W1, (aReductOfIn0 W1 W0 (xR)))))) \/ (aNormalFormOfIn0 W0 (xw) (xR))))) (aElement0 (xw)) ### Imply 3 7 % 0.61/0.80 9. (All W1, ((aElement0 W1) => (Ex W2, (aNormalFormOfIn0 W2 W1 (xR))))) (aElement0 (xw)) (-. (Ex W0, (((aElement0 W0) /\ ((((xw) = W0) \/ ((aReductOfIn0 W0 (xw) (xR)) \/ ((Ex W1, ((aElement0 W1) /\ ((aReductOfIn0 W1 (xw) (xR)) /\ (sdtmndtplgtdt0 W1 (xR) W0)))) \/ ((sdtmndtplgtdt0 (xw) (xR) W0) \/ (sdtmndtasgtdt0 (xw) (xR) W0))))) /\ (-. (Ex W1, (aReductOfIn0 W1 W0 (xR)))))) \/ (aNormalFormOfIn0 W0 (xw) (xR))))) ### All 8 % 0.61/0.80 10. (((aRewritingSystem0 (xR)) /\ (isTerminating0 (xR))) => (All W1, ((aElement0 W1) => (Ex W2, (aNormalFormOfIn0 W2 W1 (xR)))))) (-. (Ex W0, (((aElement0 W0) /\ ((((xw) = W0) \/ ((aReductOfIn0 W0 (xw) (xR)) \/ ((Ex W1, ((aElement0 W1) /\ ((aReductOfIn0 W1 (xw) (xR)) /\ (sdtmndtplgtdt0 W1 (xR) W0)))) \/ ((sdtmndtplgtdt0 (xw) (xR) W0) \/ (sdtmndtasgtdt0 (xw) (xR) W0))))) /\ (-. (Ex W1, (aReductOfIn0 W1 W0 (xR)))))) \/ (aNormalFormOfIn0 W0 (xw) (xR))))) (aElement0 (xw)) (isTerminating0 (xR)) (aRewritingSystem0 (xR)) ### DisjTree 1 2 9 % 0.61/0.80 11. (All W0, (((aRewritingSystem0 W0) /\ (isTerminating0 W0)) => (All W1, ((aElement0 W1) => (Ex W2, (aNormalFormOfIn0 W2 W1 W0)))))) (aRewritingSystem0 (xR)) (isTerminating0 (xR)) (aElement0 (xw)) (-. (Ex W0, (((aElement0 W0) /\ ((((xw) = W0) \/ ((aReductOfIn0 W0 (xw) (xR)) \/ ((Ex W1, ((aElement0 W1) /\ ((aReductOfIn0 W1 (xw) (xR)) /\ (sdtmndtplgtdt0 W1 (xR) W0)))) \/ ((sdtmndtplgtdt0 (xw) (xR) W0) \/ (sdtmndtasgtdt0 (xw) (xR) W0))))) /\ (-. (Ex W1, (aReductOfIn0 W1 W0 (xR)))))) \/ (aNormalFormOfIn0 W0 (xw) (xR))))) ### All 10 % 0.61/0.80 12. ((aElement0 (xw)) /\ ((((xu) = (xw)) \/ (((aReductOfIn0 (xw) (xu) (xR)) \/ (Ex W0, ((aElement0 W0) /\ ((aReductOfIn0 W0 (xu) (xR)) /\ (sdtmndtplgtdt0 W0 (xR) (xw)))))) /\ (sdtmndtplgtdt0 (xu) (xR) (xw)))) /\ ((sdtmndtasgtdt0 (xu) (xR) (xw)) /\ ((((xv) = (xw)) \/ (((aReductOfIn0 (xw) (xv) (xR)) \/ (Ex W0, ((aElement0 W0) /\ ((aReductOfIn0 W0 (xv) (xR)) /\ (sdtmndtplgtdt0 W0 (xR) (xw)))))) /\ (sdtmndtplgtdt0 (xv) (xR) (xw)))) /\ (sdtmndtasgtdt0 (xv) (xR) (xw)))))) (-. (Ex W0, (((aElement0 W0) /\ ((((xw) = W0) \/ ((aReductOfIn0 W0 (xw) (xR)) \/ ((Ex W1, ((aElement0 W1) /\ ((aReductOfIn0 W1 (xw) (xR)) /\ (sdtmndtplgtdt0 W1 (xR) W0)))) \/ ((sdtmndtplgtdt0 (xw) (xR) W0) \/ (sdtmndtasgtdt0 (xw) (xR) W0))))) /\ (-. (Ex W1, (aReductOfIn0 W1 W0 (xR)))))) \/ (aNormalFormOfIn0 W0 (xw) (xR))))) (isTerminating0 (xR)) (aRewritingSystem0 (xR)) (All W0, (((aRewritingSystem0 W0) /\ (isTerminating0 W0)) => (All W1, ((aElement0 W1) => (Ex W2, (aNormalFormOfIn0 W2 W1 W0)))))) ### ConjTree 11 % 0.61/0.80 13. ((All W0, (All W1, (All W2, (((aElement0 W0) /\ ((aElement0 W1) /\ ((aElement0 W2) /\ ((aReductOfIn0 W1 W0 (xR)) /\ (aReductOfIn0 W2 W0 (xR)))))) => (Ex W3, ((aElement0 W3) /\ (((W1 = W3) \/ (((aReductOfIn0 W3 W1 (xR)) \/ (Ex W4, ((aElement0 W4) /\ ((aReductOfIn0 W4 W1 (xR)) /\ (sdtmndtplgtdt0 W4 (xR) W3))))) /\ (sdtmndtplgtdt0 W1 (xR) W3))) /\ ((sdtmndtasgtdt0 W1 (xR) W3) /\ (((W2 = W3) \/ (((aReductOfIn0 W3 W2 (xR)) \/ (Ex W4, ((aElement0 W4) /\ ((aReductOfIn0 W4 W2 (xR)) /\ (sdtmndtplgtdt0 W4 (xR) W3))))) /\ (sdtmndtplgtdt0 W2 (xR) W3))) /\ (sdtmndtasgtdt0 W2 (xR) W3)))))))))) /\ ((isLocallyConfluent0 (xR)) /\ ((All W0, (All W1, (((aElement0 W0) /\ (aElement0 W1)) => (((aReductOfIn0 W1 W0 (xR)) \/ ((Ex W2, ((aElement0 W2) /\ ((aReductOfIn0 W2 W0 (xR)) /\ (sdtmndtplgtdt0 W2 (xR) W1)))) \/ (sdtmndtplgtdt0 W0 (xR) W1))) => (iLess0 W1 W0))))) /\ (isTerminating0 (xR))))) (All W0, (((aRewritingSystem0 W0) /\ (isTerminating0 W0)) => (All W1, ((aElement0 W1) => (Ex W2, (aNormalFormOfIn0 W2 W1 W0)))))) (aRewritingSystem0 (xR)) (-. (Ex W0, (((aElement0 W0) /\ ((((xw) = W0) \/ ((aReductOfIn0 W0 (xw) (xR)) \/ ((Ex W1, ((aElement0 W1) /\ ((aReductOfIn0 W1 (xw) (xR)) /\ (sdtmndtplgtdt0 W1 (xR) W0)))) \/ ((sdtmndtplgtdt0 (xw) (xR) W0) \/ (sdtmndtasgtdt0 (xw) (xR) W0))))) /\ (-. (Ex W1, (aReductOfIn0 W1 W0 (xR)))))) \/ (aNormalFormOfIn0 W0 (xw) (xR))))) ((aElement0 (xw)) /\ ((((xu) = (xw)) \/ (((aReductOfIn0 (xw) (xu) (xR)) \/ (Ex W0, ((aElement0 W0) /\ ((aReductOfIn0 W0 (xu) (xR)) /\ (sdtmndtplgtdt0 W0 (xR) (xw)))))) /\ (sdtmndtplgtdt0 (xu) (xR) (xw)))) /\ ((sdtmndtasgtdt0 (xu) (xR) (xw)) /\ ((((xv) = (xw)) \/ (((aReductOfIn0 (xw) (xv) (xR)) \/ (Ex W0, ((aElement0 W0) /\ ((aReductOfIn0 W0 (xv) (xR)) /\ (sdtmndtplgtdt0 W0 (xR) (xw)))))) /\ (sdtmndtplgtdt0 (xv) (xR) (xw)))) /\ (sdtmndtasgtdt0 (xv) (xR) (xw)))))) ### ConjTree 12 % 0.61/0.80 % SZS output end Proof % 0.61/0.80 (* END-PROOF *) %------------------------------------------------------------------------------