%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : NUM410+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % Computer : n008.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 14:42:13 EDT 2022 % Result : Theorem 2.88s 3.05s % Output : Proof 2.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : NUM410+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.33 % Computer : n008.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Tue Jul 5 15:12:38 EDT 2022 % 0.13/0.34 % CPUTime : % 2.88/3.05 % SZS status Theorem % 2.88/3.05 (* PROOF-FOUND *) % 2.88/3.05 (* BEGIN-PROOF *) % 2.88/3.05 % SZS output start Proof % 2.88/3.05 1. (relation T_0) (-. (relation T_0)) ### Axiom % 2.88/3.05 2. (function T_0) (-. (function T_0)) ### Axiom % 2.88/3.05 3. (relation T_0) (-. (relation T_0)) ### Axiom % 2.88/3.05 4. (function T_0) (-. (function T_0)) ### Axiom % 2.88/3.05 5. (ordinal (relation_dom T_0)) (-. (ordinal (relation_dom T_0))) ### Axiom % 2.88/3.05 6. (-. (transfinite_sequence T_0)) (transfinite_sequence T_0) ### Axiom % 2.88/3.05 7. ((transfinite_sequence T_0) <=> (ordinal (relation_dom T_0))) (-. (transfinite_sequence T_0)) (ordinal (relation_dom T_0)) ### Equiv 5 6 % 2.88/3.05 8. (((relation T_0) /\ (function T_0)) => ((transfinite_sequence T_0) <=> (ordinal (relation_dom T_0)))) (ordinal (relation_dom T_0)) (-. (transfinite_sequence T_0)) (function T_0) (relation T_0) ### DisjTree 3 4 7 % 2.88/3.05 9. (All A, (((relation A) /\ (function A)) => ((transfinite_sequence A) <=> (ordinal (relation_dom A))))) (relation T_0) (function T_0) (-. (transfinite_sequence T_0)) (ordinal (relation_dom T_0)) ### All 8 % 2.88/3.05 10. (-. (subset (relation_rng T_0) (relation_rng T_0))) ### Refl(subset) % 2.88/3.05 11. (-. (transfinite_sequence_of T_0 (relation_rng T_0))) (transfinite_sequence_of T_0 (relation_rng T_0)) ### Axiom % 2.88/3.05 12. ((transfinite_sequence_of T_0 (relation_rng T_0)) <=> (subset (relation_rng T_0) (relation_rng T_0))) (-. (transfinite_sequence_of T_0 (relation_rng T_0))) ### Equiv 10 11 % 2.88/3.05 13. (((relation T_0) /\ ((function T_0) /\ (transfinite_sequence T_0))) => ((transfinite_sequence_of T_0 (relation_rng T_0)) <=> (subset (relation_rng T_0) (relation_rng T_0)))) (-. (transfinite_sequence_of T_0 (relation_rng T_0))) (ordinal (relation_dom T_0)) (All A, (((relation A) /\ (function A)) => ((transfinite_sequence A) <=> (ordinal (relation_dom A))))) (function T_0) (relation T_0) ### DisjTree 1 2 9 12 % 2.88/3.05 14. (All B, (((relation B) /\ ((function B) /\ (transfinite_sequence B))) => ((transfinite_sequence_of B (relation_rng T_0)) <=> (subset (relation_rng B) (relation_rng T_0))))) (relation T_0) (function T_0) (All A, (((relation A) /\ (function A)) => ((transfinite_sequence A) <=> (ordinal (relation_dom A))))) (ordinal (relation_dom T_0)) (-. (transfinite_sequence_of T_0 (relation_rng T_0))) ### All 13 % 2.88/3.05 15. (All A, (All B, (((relation B) /\ ((function B) /\ (transfinite_sequence B))) => ((transfinite_sequence_of B A) <=> (subset (relation_rng B) A))))) (-. (transfinite_sequence_of T_0 (relation_rng T_0))) (ordinal (relation_dom T_0)) (All A, (((relation A) /\ (function A)) => ((transfinite_sequence A) <=> (ordinal (relation_dom A))))) (function T_0) (relation T_0) ### All 14 % 2.88/3.05 16. (-. (((relation T_0) /\ (function T_0)) => ((ordinal (relation_dom T_0)) => (transfinite_sequence_of T_0 (relation_rng T_0))))) (All A, (((relation A) /\ (function A)) => ((transfinite_sequence A) <=> (ordinal (relation_dom A))))) (All A, (All B, (((relation B) /\ ((function B) /\ (transfinite_sequence B))) => ((transfinite_sequence_of B A) <=> (subset (relation_rng B) A))))) ### ConjTree 15 % 2.88/3.05 17. (-. (All A, (((relation A) /\ (function A)) => ((ordinal (relation_dom A)) => (transfinite_sequence_of A (relation_rng A)))))) (All A, (All B, (((relation B) /\ ((function B) /\ (transfinite_sequence B))) => ((transfinite_sequence_of B A) <=> (subset (relation_rng B) A))))) (All A, (((relation A) /\ (function A)) => ((transfinite_sequence A) <=> (ordinal (relation_dom A))))) ### NotAllEx 16 % 2.88/3.05 % SZS output end Proof % 2.88/3.05 (* END-PROOF *) %------------------------------------------------------------------------------